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value | id int64 11.7k 11.7k ⌀ | prompt listlengths 2 2 | answer stringclasses 4
values | prompt__example_annotation__metadata dict | task_source stringclasses 1
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[
{
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"value": "$2 \\cdot 131$ The number of roots of the equation $\\sqrt{x^{2}+12 x+36}+x+6=0$ is\n(A) 0.\n(B) 2.\n(C) 4.\n(D) Infinitely many.\n(3rd \"Five Sheep Cup\" Junior High School Mathematics Competition, 1991)"
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try ... | $2 \cdot 131$ The number of roots of the equation $\sqrt{x^{2}+12 x+36}+x+6=0$ is
(A) 0.
(B) 2.
(C) 4.
(D) Infinitely many.
(3rd "Five Sheep Cup" Junior High School Mathematics Competition, 1991) | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | D | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | openthoughts | openthoughts | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\n### Step-by-Step Plan\n\n1. **Rewrite the Equation**: Start by rewriting the given equation for clarity:\n \\[\n \\sqrt{x^2 + 12x + 36} + x + 6 = 0\n \\]\n\n2. **Simplify th... | [
true
] | [
"D"
] | plan_and_execute_rationalized | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer. The model correctly analyzed the equation by breaking it down into two cases based on the absolute value. It correctly identified that \\(x = -6\\) is a valid solution in the first case, and that any \\(x < -6\\) is a solution in the second case. The conclusion that there are infinitely ... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.212:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vllm... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"from": "user",
"value": "$2 \\cdot 131$ The number of roots of the equation $\\sqrt{x^{2}+12 x+36}+x+6=0$ is\n(A) 0.\n(B) 2.\n(C) 4.\n(D) Infinitely many.\n(3rd \"Five Sheep Cup\" Junior High School Mathematics Competition, 1991)"
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try ... | $2 \cdot 131$ The number of roots of the equation $\sqrt{x^{2}+12 x+36}+x+6=0$ is
(A) 0.
(B) 2.
(C) 4.
(D) Infinitely many.
(3rd "Five Sheep Cup" Junior High School Mathematics Competition, 1991) | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | D | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | openthoughts | openthoughts | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\n### Step-by-Step Plan\n\n1. **Rewrite the Equation**: Start by rewriting the given equation for clarity:\n \\[\n \\sqrt{x^2 + 12x + 36} + x + 6 = 0\n \\]\n\n2. **Simplify In... | [
true
] | [
"D"
] | plan_and_execute_rationalized | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer. The model correctly identified that the equation simplifies to \\(|x + 6| + x + 6 = 0\\). It then analyzed the two cases separately and concluded that there are infinitely many solutions. The steps taken were logical and thorough, leading to the conclusion that the number of roots is ind... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.212:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vllm... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"from": "user",
"value": "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following propositions is correct?\n\nA: If $|\\overrightarrow{a}| > |\\overrightarrow{b}|$ and $\\overrightarrow{a}$ is in the same direction as $\\overrightarrow{b}$, then $\\overrightarrow{a} > \... | For any two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$, which of the following propositions is correct?
A: If $|\overrightarrow{a}| > |\overrightarrow{b}|$ and $\overrightarrow{a}$ is in the same direction as $\overrightarrow{b}$, then $\overrightarrow{a} > \overrightarrow{b}$.
B: $|\overrightarrow{a} + \o... | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | B | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | openthoughts | openthoughts | [
"Let's analyze each proposition one by one:\n\n**Proposition A:** If \\( |\\overrightarrow{a}| > |\\overrightarrow{b}| \\) and \\(\\overrightarrow{a}\\) is in the same direction as \\(\\overrightarrow{b}\\), then \\(\\overrightarrow{a} > \\overrightarrow{b}\\).\n\nVectors cannot be compared using inequality symbols... | [
true
] | [
"B"
] | original_rationalized | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer: The model correctly identified Proposition B as the correct statement among the options. It explained why Proposition A is incorrect due to the inability to order vectors, why Proposition C is incorrect because of the issue with the zero vector, and why Proposition D is incorrect due to ... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.212:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vllm... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Let's analyze each proposition one by one:\n\n**Proposition A:** If \\( |\\overrightarrow{a}| > |\(...TRUNCATED) | [
true
] | [
"B"
] | original_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer: The model response correctly identifies that vectors cannot be compared(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.212:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Let's analyze each proposition one by one:\n\n**Proposition A:** If \\( |\\overrightarrow{a}| > |\(...TRUNCATED) | [
true
] | [
"B"
] | original_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer: The model correctly identified Proposition B as the correct proposition(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.212:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Let's analyze each proposition one by one:\n\n**Proposition A:** If \\(|\\overrightarrow{a}| > |\\(...TRUNCATED) | [
true
] | [
"B"
] | original_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer: The model correctly analyzed each proposition and provided clear reason(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.212:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["First, I'll try to understand the problem better by writing out a plan and go really deep into det(...TRUNCATED) | [
false
] | [
"(B)"
] | plan_and_execute_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model response correctly identifies that Proposition A is incorrect(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.212:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["First, I'll try to understand the problem better by writing out a plan and go really deep into det(...TRUNCATED) | [
true
] | [
"B"
] | plan_and_execute_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer: The model correctly identifies that proposition B, stating \\( |\\overr(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.212:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["First, I'll try to understand the problem better by writing out a plan and go really deep into det(...TRUNCATED) | [
false
] | [
"(B)"
] | plan_and_execute_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model response correctly identifies Proposition B as the correct on(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.212:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["First, I'll try to understand the problem better by writing out a plan and go really deep into det(...TRUNCATED) | [
true
] | [
"B"
] | plan_and_execute_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model correctly identified that proposition B is the correct one. I(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.212:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
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