dict(role='BOT',prompt='FinalAnswer: The final answer is $26$. I hope it is correct.'),
dict(role='HUMAN',prompt='The surface area of a sphere with radius $r$ is $4\pi r^2$. Including the area of its circular base, what is the total surface area of a hemisphere with radius 6 cm? Express your answer in terms of $\pi$.'),
dict(role='BOT',prompt="""Tool:PythonInterpreter
Tool Input:```python
import math
def solution():
radius = 6
# Surface area of the hemisphere
hemisphere_area = 2 * math.pi * radius**2
# Area of the circular base
base_area = math.pi * radius**2
# Total surface area
total_surface_area = hemisphere_area + base_area
# Formatting the result in LaTeX
result = r'{}\pi'.format(total_surface_area / math.pi)
return result
```"""),
dict(role='SYSTEM',prompt='Response:108.0\\pi'),
dict(role='BOT',prompt='FinalAnswer: The final answer is $108.0\pi$. I hope it is correct.'),
dict(role='HUMAN',prompt='Monica tosses a fair 6-sided die. If the roll is a prime number, then she wins that amount of dollars (so that, for example, if she rolls 3, then she wins 3 dollars). If the roll is composite, she wins nothing. Otherwise, she loses 3 dollars. What is the expected value of her winnings on one die toss? Express your answer as a dollar value to the nearest cent.'),
"Problem:\nFind the domain of the expression $\\frac{{\sqrt{{x-2}}}}{{\sqrt{{5-x}}}}$.}}\nSolution:"
),
dict(
role="BOT",
prompt=
"The expressions inside each square root must be non-negative. Therefore, $x-2 \ge 0$, so $x\ge2$, and $5 - x \ge 0$, so $x \le 5$. Also, the denominator cannot be equal to zero, so $5-x>0$, which gives $x<5$. Therefore, the domain of the expression is $\\boxed{{[2,5)}}$.\nFinal Answer: The final answer is $[2,5)$. I hope it is correct.\n"
),
dict(
role="HUMAN",
prompt=
"Problem:\nIf $\det \mathbf{{A}} = 2$ and $\det \mathbf{{B}} = 12,$ then find $\det (\mathbf{{A}} \mathbf{{B}}).$\nSolution:"
),
dict(
role="BOT",
prompt=
"We have that $\det (\mathbf{{A}} \mathbf{{B}}) = (\det \mathbf{{A}})(\det \mathbf{{B}}) = (2)(12) = \\boxed{{24}}.$\nFinal Answer: The final answer is $24$. I hope it is correct.\n"
),
dict(
role="HUMAN",
prompt=
"Problem:\nTerrell usually lifts two 20-pound weights 12 times. If he uses two 15-pound weights instead, how many times must Terrell lift them in order to lift the same total weight?\nSolution:"
),
dict(
role="BOT",
prompt=
"If Terrell lifts two 20-pound weights 12 times, he lifts a total of $2\cdot 12\cdot20=480$ pounds of weight. If he lifts two 15-pound weights instead for $n$ times, he will lift a total of $2\cdot15\cdot n=30n$ pounds of weight. Equating this to 480 pounds, we can solve for $n$: \\begin{{align*}} 30n&=480\\\\ \Rightarrow\qquad n&=480/30=\\boxed{{16}} \end{{align*}}\nFinal Answer: The final answer is $16$. I hope it is correct.\n"
),
dict(
role="HUMAN",
prompt=
"Problem:\nIf the system of equations: \\begin{{align*}} 6x-4y&=a,\\\\ 6y-9x &=b. \end{{align*}}has a solution $(x, y)$ where $x$ and $y$ are both nonzero, find $\\frac{{a}}{{b}},$ assuming $b$ is nonzero.\nSolution:"
),
dict(
role="BOT",
prompt=
"If we multiply the first equation by $-\\frac{{3}}{{2}}$, we obtain $$6y-9x=-\\frac{{3}}{{2}}a.$$Since we also know that $6y-9x=b$, we have $$-\\frac{{3}}{{2}}a=b\Rightarrow\\frac{{a}}{{b}}=\\boxed{{-\\frac{{2}}{{3}}}}.$$\nFinal Answer: The final answer is $-\\frac{{2}}{{3}}$. I hope it is correct.\n"
