from .few_shot_prompting import FewShotPrompting few_shot_prompt = """ Problem: Subproblem 0: What is the net charge of arginine in a solution of $\\mathrm{pH} 1.0$? Please format your answer as +n or -n. Solution: The answer is +2. Final answer: The final answer is $\\boxed{+2}$. I hope it is correct. Problem: Subproblem 0: Let $z = 1 + \\sqrt{3} i$. Find $a, b$ that satisfy the equation $z^4 = a + bi$. Express your answer as the ordered pair $(a,b)$. Solution: $z^{4}$ has argument $4 \\pi / 3$ and radius 16 , so it's equal to $-8-8 \\sqrt{3} i$. Thus $a = -8, b = -8\\sqrt 3$, and our answer is $(-8, -8\\sqrt{3})$. Final answer: The final answer is $\\boxed{(-8, -8\\sqrt{3})}$. I hope it is correct. Problem: Preamble: For each Laplace Transform \\(Y(s)\\), find the function \\(y(t)\\): Subproblem 0: \\[Y(s)=\\frac{1}{(s+a)(s+b)}\\] Solution: We can simplify with partial fractions: \\[Y(s)=\\frac{1}{(s+a)(s+b)}=\\frac{C}{s+a}+\\frac{D}{s+b}\\] find the constants \\(C\\) and \\(D\\) by setting \\(s=-a\\) and \\(s=-b\\) \\[ \\begin{aligned} \\frac{1}{(s+a)(s+b)} &=\\frac{C}{s+a}+\\frac{D}{s+b} \\\\ 1 &=C(s+b)+D(s+a) \\\\ C &=\\frac{1}{b-a} \\\\ D &=\\frac{1}{a-b} \\end{aligned} \\] therefore \\[ Y(s)=\\frac{1}{b-a} \\frac{1}{s+a}-\\frac{1}{b-a} \\frac{1}{s+b} \\] By looking up the inverse Laplace Transform of \\(\\frac{1}{s+b}\\), we find the total solution \\(y(t)\\) \\[ y(t)=\\frac{e^{-a t}-e^{-b t}}{b-a} \\]. Final answer: The final answer is $\\boxed{\\frac{e^{-a t}-e^{-b t}}{b-a}}$. I hope it is correct. Problem: Preamble: The following subproblems refer to the differential equation $\\ddot{x}+b \\dot{x}+x=0$. Subproblem 0: What is the characteristic polynomial $p(s)$ of $\\ddot{x}+b \\dot{x}+x=0$? Solution: The characteristic polynomial is $p(s)=s^{2}+b s+1$. Final answer: The final answer is $\\boxed{s^{2}+b s+1}$. I hope it is correct. """.strip() few_shot_prompt = """ Problem: Subproblem 0: What is the net charge of arginine in a solution of $\\mathrm{pH} 1.0$? Please format your answer as +n or -n. Solution: The answer is +2. Final answer: The final answer is +2. I hope it is correct. Problem: Subproblem 0: Let $z = 1 + \\sqrt{3} i$. Find $a, b$ that satisfy the equation $z^4 = a + bi$. Express your answer as the ordered pair $(a,b)$. Solution: $z^{4}$ has argument $4 \\pi / 3$ and radius 16 , so it's equal to $-8-8 \\sqrt{3} i$. Thus $a = -8, b = -8\\sqrt 3$, and our answer is $\\boxed{(-8, -8\\sqrt{3})}$. Final answer: The final answer is (-8, -8\\sqrt{3}). I hope it is correct. Problem: Preamble: For each Laplace Transform \\(Y(s)\\), find the function \\(y(t)\\): Subproblem 0: \\[Y(s)=\\boxed{\\frac{1}{(s+a)(s+b)}}\\] Solution: We can simplify with partial fractions: \\[Y(s)=\\frac{1}{(s+a)(s+b)}=\\frac{C}{s+a}+\\frac{D}{s+b}\\] find the constants \\(C\\) and \\(D\\) by setting \\(s=-a\\) and \\(s=-b\\) \\[ \\begin{aligned} \\frac{1}{(s+a)(s+b)} &=\\frac{C}{s+a}+\\frac{D}{s+b} \\\\ 1 &=C(s+b)+D(s+a) \\\\ C &=\\frac{1}{b-a} \\\\ D &=\\frac{1}{a-b} \\end{aligned} \\] therefore \\[ Y(s)=\\frac{1}{b-a} \\frac{1}{s+a}-\\frac{1}{b-a} \\frac{1}{s+b} \\] By looking up the inverse Laplace Transform of \\(\\frac{1}{s+b}\\), we find the total solution \\(y(t)\\) \\[ y(t)=\\boxed{\\frac{1}{b-a}\\left(e^{-a t}-e^{-b t}\\right)} \\]. Final answer: The final answer is \\[\\frac{1}{b-a}\\left(e^{-a t}-e^{-b t}\\right)\\]. I hope it is correct. Problem: Preamble: The following subproblems refer to the differential equation $\\ddot{x}+b \\dot{x}+x=0$. Subproblem 0: What is the characteristic polynomial $p(s)$ of $\\ddot{x}+b \\dot{x}+x=0$? Solution: The characteristic polynomial is $p(s)=\\boxed{s^{2}+b s+1}$. Final answer: The final answer is $s^{2}+b s+1$. I hope it is correct. """.strip() class OCWCoursesPrompt(FewShotPrompting): def __init__(self): super().__init__() def format_prompt(self, task_input, task_output): prompt = f"{few_shot_prompt}\n\nProblem:\n{task_input}\nSolution:\n{task_output}" return prompt.rstrip() def stop_words(self): return ["\nProblem:"]