dict(role='HUMAN',prompt='Question: Here is a multiple-choice question about mathematics. Please reason through it step by step, and at the end, provide your answer option with "Therefore, the correct answer is option X", Where "X" is the correct option you think from A，B，C，D. Here is the question you need to answer:\n{question}\nLet\'s think step by step:'),
],
'single_choice_en':[
dict(role='HUMAN',prompt='Question: Here is a multiple-choice question about mathematics. Please provide the correct answer option directly.\nHere is the question you need to answer:\n{question}\nThe answer is:'),
],
'cloze_en':[
dict(role='HUMAN',prompt='{question}\nPlease reason step by step, and put your final answer within \\boxed{}.'),
dict(role='HUMAN',prompt='Question: Given that $i$ is the imaginary unit and $z$ is a complex number, $2 + \\frac{1}{i} = z(3 + i)$, the point corresponding to $z$ in the complex plane is located in the ______\nA. First quadrant\nB. Second quadrant\nC. Third quadrant\nD. Fourth quadrant'),
dict(role='BOT',prompt='Response: D'),
dict(role='HUMAN',prompt='Question: The graph of the function $y = \\tan(\\omega x - 1)$ is shifted 2 units to the left and coincides with the graph of the function $y = \\tan(\\omega x + 3)$. The minimum value of $\\omega$ is ______\nA. $2 - \\frac{\\pi}{2}$\nB. 1\nC. $\\pi - 2$\nD. 2'),
dict(role='BOT',prompt='Response: D'),
dict(role='HUMAN',prompt='Question: If $(1 + 2i)a + b = 2i$, where $a$ and $b$ are real numbers, then ______\nA. $a = 1, b = -1$\nB. $a = 1, b = 1$\nC. $a = -1, b = 1$\nD. $a = -1, b = -1$'),
dict(role='BOT',prompt='Response: A'),
dict(role='HUMAN',prompt='Question: The radius of a cone is 2 and its height is 4. A cylinder has its lower base on the base of the cone and its upper base on the lateral surface of the cone. When the lateral surface area of the cylinder is $4\\pi$, the volume of the cylinder is ______\nA. $\\pi$\nB. $2\\pi$\nC. $3\\pi$\nD. $4\\pi$'),
dict(role='BOT',prompt='Response: B'),
dict(role='HUMAN',prompt='Question: {question}'),
dict(role='BOT',prompt='Response: {answer}'),
],
'single_choice_en_with_reasoning':[
dict(role='HUMAN',prompt='Question: Given that $i$ is the imaginary unit and $z$ is a complex number, $2 + \\frac{1}{i} = z(3 + i)$, the point corresponding to $z$ in the complex plane is located in the ______\nA. First quadrant\nB. Second quadrant\nC. Third quadrant\nD. Fourth quadrant'),
dict(role='BOT',prompt='Response: First, we multiply both sides of the equation by the conjugate of $(3 + i)$: $z = \\frac{2 - i}{3 + i} \\cdot \\frac{3 - i}{3 - i}$. We perform the multiplication: $z = \\frac{(2 - i)(3 - i)}{(3 + i)(3 - i)}$, $z = \\frac{6 - 2i - 3i + i^2}{9 - 3i + 3i - i^2}$. Since $i^2 = -1$, we can simplify this further: $z = \\frac{6 - 5i - 1}{9 + 1}$ $z = \\frac{1}{2} - \\frac{1}{2}i$. In the complex plane, this point is located in the fourth quadrant, because its real part is positive ($\\frac{1}{2}$) and its imaginary part is negative ($-\\frac{1}{2}$)\nAnswer option: D'),
dict(role='HUMAN',prompt='Question: The graph of the function $y = \\tan(\\omega x - 1)$ is shifted 2 units to the left and coincides with the graph of the function $y = \\tan(\\omega x + 3)$. The minimum value of $\\omega$ is ______\nA. $2 - \\frac{\\pi}{2}$\nB. 1\nC. $\\pi - 2$\nD. 2'),
dict(role='BOT',prompt='Response: In order for the graph of this new function to coincide with the graph of $y = \\tan(\\omega x + 3)$, we need to satisfy the following condition: $\\tan(\\omega(x + 2) - 1) = \\tan(\\omega x + 3)$. Therefore, we can write: $\\omega(x + 2) - 1 = \\omega x + 3 + k\\pi$. Solving this equation, we get: $\\omega x + 2\\omega - 1 = \\omega x + 3 + k\\pi$. $2\\omega - 1 = 3 + k\\pi$. $\\omega = 2 + \\frac{k\\pi}{2}$. Since $\\omega > 0$, we need to find the smallest positive integer $k$ that satisfies the condition. When $k = 0$, we get $\\omega = 2$, which is the smallest positive value that satisfies the condition. Therefore, the minimum value is 2. Answer option: D'),
dict(role='HUMAN',prompt='Question: If $(1 + 2i)a + b = 2i$, where $a$ and $b$ are real numbers, then ______\nA. $a = 1, b = -1$\nB. $a = 1, b = 1$\nC. $a = -1, b = 1$\nD. $a = -1, b = -1$'),
dict(role='BOT',prompt='Response: We can write this equation as: $a + 2ai + b = 2i$, and then separate the real and imaginary parts: $a + b = 0$. $2a = 2$. Since $a + b = 0$, we can get $a = -b$. Substituting this value into $2a = 2$, we get $2(-b) = 2$, so $b = -1$. Therefore, $a = 1$. Answer option: A'),
dict(role='HUMAN',prompt='Question: The radius of a cone is 2 and its height is 4. A cylinder has its lower base on the base of the cone and its upper base on the lateral surface of the cone. When the lateral surface area of the cylinder is $4\\pi$, the volume of the cylinder is ______\nA. $\\pi$\nB. $2\\pi$\nC. $3\\pi$\nD. $4\\pi$'),
dict(role='BOT',prompt='Response: We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem tells us that if the two sides of a triangle are $a$ and $b$, then the length of the third side is $c = \\sqrt{a^2 + b^2}$. In this problem, $a = 3$ and $b = 4$, so $c = \\sqrt{3^2 + 4^2} = \\sqrt{9 + 16} = \\sqrt{25} = 5$. Answer option: A'),
dict(role='HUMAN',prompt='Question: Shawn has five toys. For Christmas, he got two toys each from his mom and dad. How many toys does he have now?'),
dict(role='BOT',prompt='Response: He has 5 toys. He got 2 from mom, so after that he has 5 + 2 = 7 toys. Then he got 2 more from dad, so in total he has 7 + 2 = 9 toys. The answer is 9.'),
dict(role='HUMAN',prompt='Question: There were nine computers in the server room. Five more computers were installed each day, from monday to thursday. How many computers are now in the server room?'),
dict(role='BOT',prompt='Response: There are 4 days from monday to thursday. 5 computers were added each day. That means in total 4 * 5 = 20 computers were added. There were 9 computers in the beginning, so now there are 9 + 20 = 29 computers. The answer is 29.'),
dict(role='HUMAN',prompt='Question: Michael had 58 golf balls. On tuesday, he lost 23 golf balls. On wednesday, he lost 2 more. How many golf balls did he have at the end of wednesday?'),
dict(role='BOT',prompt='Response: Michael initially had 58 balls. He lost 23 on Tuesday, so after that he has 58 - 23 = 35 balls. On Wednesday he lost 2 more so now he has 35 - 2 = 33 balls. The answer is 33.'),
dict(role='HUMAN',prompt='Question: Olivia has $23. She bought five bagels for $3 each. How much money does she have left?'),
dict(role='BOT',prompt='Response: She bought 5 bagels for $3 each. This means she spent 5 * $3 = $15 on the bagels. She had $23 in beginning, so now she has $23 - $15 = $8. The answer is 8.'),
ZERO_SHOT_PROMPT='You are a helpful assistant for calculating a score for a given patient note. Please think step-by-step to solve the question and then generate the required score. Your output should only contain a JSON dict formatted as {"step_by_step_thinking": str(your_step_by_step_thinking_procress_to_solve_the_question), "answer": str(short_and_direct_answer_of_the_question)}. \n Here is the patient note:\n{patient_note}\n\nHere is the task:\n{question}\n\nPlease directly output the JSON dict formatted as {"step_by_step_thinking": str(your_step_by_step_thinking_procress_to_solve_the_question), "answer": str(short_and_direct_answer_of_the_question)}:'
Answer the following multiple choice question. The last line of your response should be of the following format: 'ANSWER: $LETTER' (without quotes) where LETTER is one of Options(e.g. one of ABCDEFGHIJKLMNOP). Think step by step before answering.
Answer the following multiple choice question. The last line of your response should be of the following format: 'ANSWER: $LETTER' (without quotes) where LETTER is one of Options(e.g. one of ABCDEFGHIJKLMNOP). Think step by step before answering.
Question:\n
{question}
Options:\n
{choices}
""".strip()
GRADER_TEMPLATE="""
Please as a grading expert, judge whether the final answers given by the candidates below are consistent with the standard answers, that is, whether the candidates answered correctly.
Here are some evaluation criteria:
1. Please refer to the given standard answer. You don't need to re-generate the answer to the question because the standard answer has been given. You only need to judge whether the candidate's answer is consistent with the standard answer according to the form of the question. Don't try to answer the original question. You can assume that the standard answer is definitely correct.
2. Because the candidate's answer may be different from the standard answer in the form of expression, before making a judgment, please understand the question and the standard answer first, and then judge whether the candidate's answer is correct, but be careful not to try to answer the original question.
3. Some answers may contain multiple items, such as multiple-choice questions, multiple-select questions, fill-in-the-blank questions, etc. As long as the answer is the same as the standard answer, it is enough. For multiple-select questions and multiple-blank fill-in-the-blank questions, the candidate needs to answer all the corresponding options or blanks correctly to be considered correct.
4. Some answers may be expressed in different ways, such as some answers may be a mathematical expression, some answers may be a textual description, as long as the meaning expressed is the same. And some formulas are expressed in different ways, but they are equivalent and correct.
Please judge whether the following answers are consistent with the standard answer based on the above criteria. Grade the predicted answer of this new question as one of:
A: CORRECT
B: INCORRECT
Just return the letters "A" or "B", with no text around it.
Here is your task. Simply reply with either CORRECT, INCORRECT. Don't apologize or correct yourself if there was a mistake; we are just trying to grade the answer.
SYSTEM_PROMPT='You are a helpful medical assistant.\n\n'# Where to put this?
ZERO_SHOT_PROMPT='Q: {question}\nA: Among {start} through {end}, the answer is'
GRADER_TEMPLATE="""
Please as a grading expert, judge whether the final answers given by the candidates below are consistent with the standard answers, that is, whether the candidates answered correctly.
Here are some evaluation criteria:
1. Please refer to the given standard answer. You don't need to re-generate the answer to the question because the standard answer has been given. You only need to judge whether the candidate's answer is consistent with the standard answer according to the form of the question. Don't try to answer the original question. You can assume that the standard answer is definitely correct.
2. Because the candidate's answer may be different from the standard answer in the form of expression, before making a judgment, please understand the question and the standard answer first, and then judge whether the candidate's answer is correct, but be careful not to try to answer the original question.
3. Some answers may contain multiple items, such as multiple-choice questions, multiple-select questions, fill-in-the-blank questions, etc. As long as the answer is the same as the standard answer, it is enough. For multiple-select questions and multiple-blank fill-in-the-blank questions, the candidate needs to answer all the corresponding options or blanks correctly to be considered correct.
4. Some answers may be expressed in different ways, such as some answers may be a mathematical expression, some answers may be a textual description, as long as the meaning expressed is the same. And some formulas are expressed in different ways, but they are equivalent and correct.
Please judge whether the following answers are consistent with the standard answer based on the above criteria. Grade the predicted answer of this new question as one of:
A: CORRECT
B: INCORRECT
Just return the letters "A" or "B", with no text around it.
Here is your task. Simply reply with either CORRECT, INCORRECT. Don't apologize or correct yourself if there was a mistake; we are just trying to grade the answer.
<Original Question Begin>: Q: {question}\nA: Among {start} through {end}, the answer is\n<Original Question End>\n\n
SYSTEM_PROMPT='You are a helpful medical assistant.\n\n'# Where to put this?
ZERO_SHOT_PROMPT='Q: {question}\n Please select the correct answer from the options above and output only the corresponding letter (A, B, C, D, or E) without any explanation or additional text.\n'
SYSTEM_PROMPT='You are a helpful medical assistant.\n\n'# Where to put this?
ZERO_SHOT_PROMPT='Q: {question}\n Please select the correct answer from the options above and output only the corresponding letter (A, B, C, D, or E) without any explanation or additional text.\n'
GRADER_TEMPLATE="""
Please as a grading expert, judge whether the final answers given by the candidates below are consistent with the standard answers, that is, whether the candidates answered correctly.
Here are some evaluation criteria:
1. Please refer to the given standard answer. You don't need to re-generate the answer to the question because the standard answer has been given. You only need to judge whether the candidate's answer is consistent with the standard answer according to the form of the question. Don't try to answer the original question. You can assume that the standard answer is definitely correct.
2. Because the candidate's answer may be different from the standard answer in the form of expression, before making a judgment, please understand the question and the standard answer first, and then judge whether the candidate's answer is correct, but be careful not to try to answer the original question.
3. Some answers may contain multiple items, such as multiple-choice questions, multiple-select questions, fill-in-the-blank questions, etc. As long as the answer is the same as the standard answer, it is enough. For multiple-select questions and multiple-blank fill-in-the-blank questions, the candidate needs to answer all the corresponding options or blanks correctly to be considered correct.
4. Some answers may be expressed in different ways, such as some answers may be a mathematical expression, some answers may be a textual description, as long as the meaning expressed is the same. And some formulas are expressed in different ways, but they are equivalent and correct.
Please judge whether the following answers are consistent with the standard answer based on the above criteria. Grade the predicted answer of this new question as one of:
A: CORRECT
B: INCORRECT
Just return the letters "A" or "B", with no text around it.
Here is your task. Simply reply with either CORRECT, INCORRECT. Don't apologize or correct yourself if there was a mistake; we are just trying to grade the answer.
<Original Question Begin>: Q: {question}\nPlease select the correct answer from the options above and output only the corresponding letter (A, B, C, D, or E) without any explanation or additional text.\n\n<Original Question End>\n\n
The following introduction comes from the abstract in [NPHardEval: Dynamic Benchmark on Reasoning Ability of Large Language Models via Complexity Classes](https://arxiv.org/abs/2312.14890)
```
This benchmark is designed to evaluate the reasoning abilities of LLMs across a broad spectrum of 900 algorithmic questions, extending up to the NP-Hard complexity class. These questions are meticulously chosen to represent a wide range of complexity class below the NP-hard complexity class, offering a rigorous measure of the reasoning ability of LLMs.
```
## Official link
### Paper
[NPHardEval: Dynamic Benchmark on Reasoning Ability of Large Language Models via Complexity Classes](https://arxiv.org/abs/2312.14890)
The Graph Coloring Problem (Decision Version, GCP-D) involves determining if it is possible to color the vertices of a graph using a given number of colors, ensuring no two adjacent vertices have the same color.
Find out if the vertices of a graph with 6 vertices can be colored using only 3 colors, such that no adjacent vertices share the same color.
Provide a yes or no answer, along with a concise explanation of your reasoning. Keep your explanation focused and brief.
Enclose your output in <root></root> tags. Include your reasoning in <reasoning></reasoning> tags and the final yes/no answer in <final_answer></final_answer> tags, like <final_answer>{'Feasible': 'YES_OR_NO'}</final_answer>.
The graph is below:
Vertex 2 is connected to vertex 4.
Vertex 2 is connected to vertex 5.
Vertex 3 is connected to vertex 5.
Vertex 4 is connected to vertex 5.
Vertex 5 is connected to vertex 6.
```
Output example I (from GPT-4):
```
<root>
<final_answer>{'Feasible': 'YES'}</final_answer>
<reasoning>Yes, it is possible to color the vertices of the given graph with 6 vertices using only 3 colors, such that no adjacent vertices share the same color. The graph does not contain any triangles or cycles of length greater than 3, which means it is a planar graph. By the Four Color Theorem, any planar graph can be colored using at most 4 colors. Since we have only 3 colors available, it is feasible to color the vertices without any adjacent vertices sharing the same color.</reasoning>
</root>
```
Input example II:
```
The Traveling Salesman Problem (Decision Version, TSP-D) focuses on determining if a salesman can complete a route, visiting each city at least once, with the total travel distance being less than a specified value.
Check if it's possible for a salesman to visit each of the 10 cities at least once and return to the starting city with the total distance less than 3481.5. The distances between each pair of cities are given.
Provide a yes or no answer, with a succinct explanation of your decision process. Focus on clarity and brevity in your response.
Enclose your output in <root></root> tags. Present your reasoning in <reasoning></reasoning> tags and the final yes/no answer in <final_answer></final_answer> tags, like <final_answer>{'Feasible': 'YES_OR_NO'}</final_answer>.
The distances between cities are below:
The distance between City 0 and City 1 is 58.0.
The distance between City 0 and City 2 is 171.0.
The distance between City 0 and City 3 is 122.0.
The distance between City 0 and City 4 is 109.0.
The distance between City 0 and City 5 is 93.0.
The distance between City 0 and City 6 is 106.0.
The distance between City 0 and City 7 is 52.0.
The distance between City 0 and City 8 is 115.0.
The distance between City 0 and City 9 is 148.0.
The distance between City 1 and City 2 is 145.0.
The distance between City 1 and City 3 is 71.0.
The distance between City 1 and City 4 is 114.0.
The distance between City 1 and City 5 is 69.0.
The distance between City 1 and City 6 is 163.0.
The distance between City 1 and City 7 is 132.0.
The distance between City 1 and City 8 is 183.0.
The distance between City 1 and City 9 is 115.0.
The distance between City 2 and City 3 is 107.0.
The distance between City 2 and City 4 is 163.0.
The distance between City 2 and City 5 is 63.0.
The distance between City 2 and City 6 is 91.0.
The distance between City 2 and City 7 is 108.0.
The distance between City 2 and City 8 is 109.0.
The distance between City 2 and City 9 is 77.0.
The distance between City 3 and City 4 is 119.0.
The distance between City 3 and City 5 is 131.0.
The distance between City 3 and City 6 is 79.0.
The distance between City 3 and City 7 is 159.0.
The distance between City 3 and City 8 is 27.0.
The distance between City 3 and City 9 is 64.0.
The distance between City 4 and City 5 is 85.0.
The distance between City 4 and City 6 is 110.0.
The distance between City 4 and City 7 is 71.0.
The distance between City 4 and City 8 is 61.0.
The distance between City 4 and City 9 is 61.0.
The distance between City 5 and City 6 is 73.0.
The distance between City 5 and City 7 is 132.0.
The distance between City 5 and City 8 is 82.0.
The distance between City 5 and City 9 is 96.0.
The distance between City 6 and City 7 is 156.0.
The distance between City 6 and City 8 is 103.0.
The distance between City 6 and City 9 is 69.0.
The distance between City 7 and City 8 is 108.0.
The distance between City 7 and City 9 is 97.0.
The distance between City 8 and City 9 is 75.0.
```
Output example II (from GPT-4):
```
<root> <reasoning> The Traveling Salesman Problem is a well-known problem in the field of computer science and operations research. It is a combinatorial optimization problem, which means it involves finding the best solution from a finite set of possible solutions. The problem is NP-hard, which means there is no known algorithm that can solve it in polynomial time. Therefore, to solve this problem, we would need to use an algorithm that can find the optimal solution, such as a brute force algorithm, a genetic algorithm, or a simulated annealing algorithm. However, these algorithms can be computationally expensive, especially for large problem sizes. In this case, we have 10 cities, which means there are 10! = 3,628,800 possible routes. Therefore, without the use of a computer, it would be impractical to manually check all possible routes to find the one with the total distance less than 3481.5. </reasoning> <final_answer>{'Feasible': 'UNKNOWN'}</final_answer> </root>
Challenging the Boundaries of Reasoning: An Olympiad-Level Math Benchmark for Large Language Models by Haoxiang Sun, Yingqian Min, Zhipeng Chen, Wayne Xin Zhao, Zheng Liu, Zhongyuan Wang, Lei Fang, and Ji-Rong Wen.
Please as a grading expert, judge whether the final answers given by the candidates below are consistent with the standard answers, that is, whether the candidates answered correctly.
Here are some evaluation criteria:
1. Please refer to the given standard answer. You don't need to re-generate the answer to the question because the standard answer has been given. You only need to judge whether the candidate's answer is consistent with the standard answer according to the form of the question. Don't try to answer the original question. You can assume that the standard answer is definitely correct.
2. Because the candidate's answer may be different from the standard answer in the form of expression, before making a judgment, please understand the question and the standard answer first, and then judge whether the candidate's answer is correct, but be careful not to try to answer the original question.
3. Some answers may contain multiple items, such as multiple-choice questions, multiple-select questions, fill-in-the-blank questions, etc. As long as the answer is the same as the standard answer, it is enough. For multiple-select questions and multiple-blank fill-in-the-blank questions, the candidate needs to answer all the corresponding options or blanks correctly to be considered correct.
4. Some answers may be expressed in different ways, such as some answers may be a mathematical expression, some answers may be a textual description, as long as the meaning expressed is the same. And some formulas are expressed in different ways, but they are equivalent and correct.
5. If the prediction is given with \\boxed{}, please ignore the \\boxed{} and only judge whether the candidate's answer is consistent with the standard answer.
Please judge whether the following answers are consistent with the standard answer based on the above criteria. Grade the predicted answer of this new question as one of:
A: CORRECT
B: INCORRECT
Just return the letters "A" or "B", with no text around it.
Here is your task. Simply reply with either CORRECT, INCORRECT. Don't apologize or correct yourself if there was a mistake; we are just trying to grade the answer.
Please as a grading expert, judge whether the final answers given by the candidates below are consistent with the standard answers, that is, whether the candidates answered correctly.
Here are some evaluation criteria:
1. Please refer to the given standard answer. You don't need to re-generate the answer to the question because the standard answer has been given. You only need to judge whether the candidate's answer is consistent with the standard answer according to the form of the question. Don't try to answer the original question. You can assume that the standard answer is definitely correct.
2. Because the candidate's answer may be different from the standard answer in the form of expression, before making a judgment, please understand the question and the standard answer first, and then judge whether the candidate's answer is correct, but be careful not to try to answer the original question.
3. Some answers may contain multiple items, such as multiple-choice questions, multiple-select questions, fill-in-the-blank questions, etc. As long as the answer is the same as the standard answer, it is enough. For multiple-select questions and multiple-blank fill-in-the-blank questions, the candidate needs to answer all the corresponding options or blanks correctly to be considered correct.
4. Some answers may be expressed in different ways, such as some answers may be a mathematical expression, some answers may be a textual description, as long as the meaning expressed is the same. And some formulas are expressed in different ways, but they are equivalent and correct.
5. If the prediction is given with \\boxed{}, please ignore the \\boxed{} and only judge whether the candidate's answer is consistent with the standard answer.
Please judge whether the following answers are consistent with the standard answer based on the above criteria. Grade the predicted answer of this new question as one of:
A: CORRECT
B: INCORRECT
Just return the letters "A" or "B", with no text around it.
Here is your task. Simply reply with either CORRECT, INCORRECT. Don't apologize or correct yourself if there was a mistake; we are just trying to grade the answer.
