idx int64 1 6.08k | prompt stringlengths 754 12.1k | answers sequencelengths 8 8 | gt stringlengths 1 134 | true_reward bool 1
class | second_rewards sequencelengths 8 8 | my_solu sequencelengths 1 1 | flag bool 1
class | messages listlengths 5 5 | turn int64 5 5 | conversations listlengths 5 5 |
|---|---|---|---|---|---|---|---|---|---|---|
5,321 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Stephen's ca... | [
"The final answer is indeed \\(\\boxed{115}\\).",
"After reviewing the code and results, I re-evaluated the probability calculation. It appears that I incorrectly calculated the number of valid patterns. Let's correct this.\n\nThe correct number of valid patterns is 10, but the total number of possible combinatio... | 173 | false | [
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"<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.<|im_end|>\n<|im_start|>user\... | true | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 5 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Stephen's calculator displays only one digit. Each time he switches it on, each of the seven bars will either illuminate or not, with a probability of 0.5. The resultant display ... |
3,288 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
(Physics) In... | [
"Consider the arrangement of 9 seats with 3 families of three each (AAABBBCCC). The condition is that each family must sit together. Therefore, for each family, they form a block. Thus, the arrangement reduces to arranging 3 blocks (AAABBBCCC) in a row, which is a permutation of 3 items (3! = 6 ways). Now, within e... | (3!)^4 | false | [
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"<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.<|im_end|>\n<|im_start|>user\... | true | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 5 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(Physics) In a row of 9 seats, there are 3 families of three sitting together. If each family sits together, the number of different seating arrangements is Let's think step by s... |
4,772 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
∫_0^1(3x+{e^... | [
"It seems the integral \\(\\int_0^1 (3x + e^x) \\, dx\\) was evaluated correctly. But please, ensure the final answer is placed correctly within the required format.\n\nThe correct final answer is:\n\n\\[\n\\boxed{\\frac{1}{2} + e}\n\\]",
"The initial response was \\(\\boxed{\\frac{1}{2} + e}\\), and it was deeme... | e + \frac{1}{2} | false | [
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"<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.<|im_end|>\n<|im_start|>user\... | true | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 5 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "∫_0^1(3x+{e^x})dx Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
},
{
"content": "∫_0^1(3x+{e^x})dx\n\nTo solve the integral,... |
1,280 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Given $f(x)=... | [
"The approach to solving this problem is correct. Let's clarify the constraints and ensure the solution is accurate.\n\n1. **Finding the range of \\(f(x)\\) on \\([0,1]\\):**\n \\[\n f(x) = \\frac{2x^2}{x + 1}\n \\]\n - \\(f(0) = 0\\)\n - \\(f(1) = 1\\)\n - The derivative \\(f'(x) = \\frac{4x(x+1) - 2x^... | [\frac{5}{2}, 4] | false | [
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"<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.<|im_end|>\n<|im_start|>user\... | true | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 5 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $f(x)= \\frac{2x^{2}}{x+1}$ and $g(x)=a\\sin \\frac{πx}{2}+5-2a (a > 0)$, if for any $x\\_1\\in[0,1]$, there always exists $x\\_0\\in[0,1]$ such that $g(x\\_0)=f(x\\_1)$ ho... |
5,287 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Let $z$ be a... | [
"To solve the problem correctly, let's follow the steps carefully again. We need to find the largest possible distance between \\((1 + 2i)z^4\\) and \\(z^6\\) for a complex number \\(z\\) such that \\(|z| = 3\\).\n\nLet \\(z = 3e^{i\\theta}\\), then:\n\\[z^4 = 3^4 e^{i4\\theta} = 81 e^{i4\\theta},\\]\n\\[z^6 = 3^6 ... | 81 \times (9 + \sqrt{5}) | false | [
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"<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.<|im_end|>\n<|im_start|>user\... | true | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 5 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $z$ be a complex number such that $|z| = 3.$ Find the largest possible distance between $(1 + 2i)z^4$ and $z^6$ when plotted in the complex plane. Let's think step by step a... |
1,007 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Find the der... | [
"Apologies for the confusion. However, the solution we've worked through is correctly derived, and the error is likely in my earlier explanation. Let's review the steps and ensure the final form is correctly boxed. The derivative of the function \\( y = \\frac{1}{4} \\cdot \\ln \\frac{x-1}{x+1} - \\frac{1}{2} \\cdo... | \frac{1}{x^4 - 1} | false | [
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"<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.<|im_end|>\n<|im_start|>user\... | true | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n\nAlways ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{... | 5 | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the derivative.\n\n\\[ y = \\frac{1}{4} \\cdot \\ln \\frac{x-1}{x+1} - \\frac{1}{2} \\cdot \\operatorname{arctg} \\, x \\] Let's think step by step and output the final answ... |
2,323 | "<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these step(...TRUNCATED) | ["It appears that the initial Python solution was correct. Let's double-check the reasoning and the (...TRUNCATED) | 317 | false | [
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3,947 | "<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these step(...TRUNCATED) | ["Let's think step by step and output the final answer within \\boxed{} again.不见了\n有.\\quad\(...TRUNCATED) | 4, -\frac{1}{6}, -1, \frac{2}{3} | false | [
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2,346 | "<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these step(...TRUNCATED) | ["The code executed successfully and printed the correct answer. So, the value of \\(\\left\\lceil\\(...TRUNCATED) | 65 | false | [
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1,316 | "<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these step(...TRUNCATED) | ["Let's re-check the steps and ensure the solution is correct. The function is $f(x) = \\sin\\left( (...TRUNCATED) | 4 | false | [
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