# -- HELM prompt, 8 shot, CoT? ref: https://storage.googleapis.com/crfm-helm-public/lite/benchmark_output/runs/v1.0.0/math:subject=algebra,level=1,use_official_examples=False,use_chain_of_thought=True,model=01-ai_yi-34b/scenario_state.json, https://crfm.stanford.edu/helm/lite/latest/#/runs/math:subject=algebra,level=1,use_official_examples=False,use_chain_of_thought=True,model=01-ai_yi-34b HELM_MATH_PROMPT: str = ( """Given a mathematics problem, determine the answer. Simplify your answer as much as possible.### Problem: Let $r=3^s-s$ and $s=2^n+1$. What is the value of $r$ when $n=2$? Answer: First substitute $n=2$ into the expression for $s$ to find $s=2^2+1=5$. Then substitute $s=5$ into the expression for $r$ to find $r=3^5-5=243-5=\\boxed{238}.### Problem: If$x^{2y}= 4$and$x = 4$, what is the value of$y$? Express your answer as a common fraction. Answer: Plugging$x = 4$into the first equation, we get$4^{2y} = 4^1 \\Rightarrow 2y = 1 \\Rightarrow y = \\boxed{\\frac{1}{2}}.### Problem: If $y = \\displaystyle\\frac{1}{3x+1}$, what is the value of $x$ when $y = 1$? Answer: Since $y=1$, we have $1 =\\displaystyle\\frac{1}{3x+1}$. Multiplying both sides by $3x+1$, we have $$3x+1=1$$ $$\\Rightarrow \\qquad 3x=0$$ $$\\Rightarrow \\qquad x=\\boxed{0}$$### Problem: A scale drawing of a park shows that one inch represents 800 feet. A line segment in the drawing that is 4.75 inches long represents how many feet? Answer: Each inch of the 4.75-inch line segment represents 800 feet, so the whole line segment represents $4.75\\times800=\\frac{19}{4}\\cdot800=19\\cdot200=\\boxed{3800}$ feet.### Problem: If $(x + y)^2 = 25$ and $xy = 6$, what is the value of $x^2 + y^2$? Answer: We know that $(x + y)^2 = (x^2 + y^2) + 2xy = 25$. We are given that $xy = 6$. So, by substitution, $x^2 + y^2 + 2xy = x^2 + y^2 + 2(6) = 25$. It follows that $x^2 + y^2 = 25 - 12 = \\boxed{13}$.### Problem: On a hot day, Megan likes to eat a Popsicle every 15 minutes. Assuming she keeps up that rate of consumption, how many Popsicles can Megan finish in 4 hours and 30 minutes? Answer: Let $p$ be the number of Popsicles Megan can finish in 4 hours and 30 minutes. If we convert that period of time into minutes, we find that 4 hours and 30 minutes is equal to $(4)(60)+30=270$ minutes. From here, we can set up the proportion \\begin{align*} \\frac{x}{270}& =\\frac{1}{15}\\\\\\Rightarrow \\qquad x& =\\left(\\frac{1}{15}\\right)(270)\\\\\\Rightarrow \\qquad x& =\\boxed{18}\\end{align*}### Problem: Compute $95^2$ in your head. Answer: We have $(90 + 5)^2 = 90^2 + 2(90)(5) + 5^2 = 8100 + 900 + 25 = \\boxed{9025}$.### Problem: If $2^8=16^x$, find $x$. Answer: We can write $16$ as $2^4$. Therefore, we can write our equation as $2^8 = 2^{4 \\cdot x}$. Solving, we get that $x = \\boxed{2}$.### Problem: {problem} Answer:""")