conversations listlengths 2 2 | question stringlengths 32 1.34k | source null | id null | prompt listlengths 2 2 | answer stringclasses 519
values | prompt__example_annotation__metadata dict | task_source stringclasses 1
value | task_config stringclasses 1
value | model_responses__example_annotation listlengths 1 1 | model_responses__example_annotation__eval_is_correct listlengths 1 1 | model_responses__example_annotation__eval_extracted_answers listlengths 1 1 | prompt_type stringclasses 2
values | reflection_prompt listlengths 2 2 | model_responses__mutated_prompts_reflection listlengths 1 1 | model_responses__mutated_prompts_reflection__finish_reason_length_flags listlengths 1 1 | model_responses__mutated_prompts_reflection__length_partial_responses listlengths 1 1 | reflection_prompt__mutated_prompts_reflection__metadata dict | model_responses__mutated_prompts_reflection__metadata dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[
{
"from": "user",
"value": "Given that the domains of functions $f(x)$ and $g(x)$ are both $\\mathbb{R}$, $f(x+1)$ is an odd function, and $f(1-x) + g(x) = 2$, $f(x) + g(x-3) = 2$, find $\\sum_{k=1}^{24}g(k)$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's try to tackle this problem s... | Given that the domains of functions $f(x)$ and $g(x)$ are both $\mathbb{R}$, $f(x+1)$ is an odd function, and $f(1-x) + g(x) = 2$, $f(x) + g(x-3) = 2$, find $\sum_{k=1}^{24}g(k)$. | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 48 | {
"api_url": "http://10.32.36.236:9080/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 | [
"Rewritten Question: Given that \\( f(x+1) \\) is an odd function, and \\( f(1-x) + g(x) = 2 \\), \\( f(x) + g(x-3) = 2 \\), find \\( \\sum_{k=1}^{24} g(k) \\).\n\nStep-by-step solution:\n1. Since \\( f(x+1) \\) is an odd function, we have \\( f(-x+1) = -f(x+1) \\).\n2. From the given equations:\n \\[ f(1-x) + g(... | [
true
] | [
"48"
] | rephrase | [
{
"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 response correctly deduced that \\( g(k) \\) is periodic with period 4. It found that the sum of \\( g(k) \\) over one period (i.e., \\( g(1) + g(2) + g(3) + g(4) \\)) is 8. Consequently, the sum over 24 terms (6 periods) is \\( 6 \\times 8 = 48 \\). The logic followed to arriv... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.207:10080/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_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"from": "user",
"value": "Given that the domains of functions $f(x)$ and $g(x)$ are both $\\mathbb{R}$, $f(x+1)$ is an odd function, and $f(1-x) + g(x) = 2$, $f(x) + g(x-3) = 2$, find $\\sum_{k=1}^{24}g(k)$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's try to tackle this problem s... | Given that the domains of functions $f(x)$ and $g(x)$ are both $\mathbb{R}$, $f(x+1)$ is an odd function, and $f(1-x) + g(x) = 2$, $f(x) + g(x-3) = 2$, find $\sum_{k=1}^{24}g(k)$. | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 48 | {
"api_url": "http://10.32.36.236:9080/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 | [
"Rewritten Question: Given \\( f(x+1) \\) is an odd function, \\( f(1-x) + g(x) = 2 \\), and \\( f(x) + g(x-3) = 2 \\), find \\( \\sum_{k=1}^{24} g(k) \\).\n\nStep 1: Analyze the properties of \\( f(x) \\).\nSince \\( f(x+1) \\) is an odd function, we have:\n\\[ f(-x+1) = -f(x+1). \\]\nLet's substitute \\( x = y - ... | [
false
] | [
"32"
] | rephrase | [
{
"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 solution provided correctly deduces the periodic nature of \\(g(x)\\) and the fact that \\(g(1) + g(2) + g(3) + g(4) = 8\\). It further concludes that since \\(g(x)\\) is periodic with period 4, the sum \\(\\sum_{k=1}^{24} g(k)\\) will be \\(6 \\times 8 = 48\\). The working is consis... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.207:10080/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_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given that the domains of functions $f(x)$ and $g(x)$ are both $\\mathbb{R}(...TRUNCATED) | "Given that the domains of functions $f(x)$ and $g(x)$ are both $\\mathbb{R}$, $f(x+1)$ is an odd fu(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 48 | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To solve for \\(\\sum_{k=1}^{24}g(k)\\), we start with the given conditions:\n1. \\(f(x+1)\\) is a(...TRUNCATED) | [
true
] | [
"48"
] | alternative | [{"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 \\(f(x)\\) is periodic with a perio(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given that the domains of functions $f(x)$ and $g(x)$ are both $\\mathbb{R}(...TRUNCATED) | "Given that the domains of functions $f(x)$ and $g(x)$ are both $\\mathbb{R}$, $f(x+1)$ is an odd fu(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 48 | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To solve the problem, we need to analyze the given conditions and derive useful information about (...TRUNCATED) | [
false
] | [
"12"
] | alternative | [{"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 concludes that the sum of \\(g(k)\\) from \\(k=1\\) (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"(Turkey TST 2013 P2)\n\nFind all functions $f: \\mathbb{R} \\rightarrow \\m(...TRUNCATED) | "(Turkey TST 2013 P2)\n\nFind all functions $f: \\mathbb{R} \\rightarrow \\mathbb{R}_{+}^{*}$ such t(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | x^2 + x + 1 | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Find all functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R}_{+}^{*} \\) suc(...TRUNCATED) | [
false
] | [
"f(x) = 2x + 1"
] | rephrase | [{"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 concludes that the function \\( f(x) = x^2 + x + 1(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"(Turkey TST 2013 P2)\n\nFind all functions $f: \\mathbb{R} \\rightarrow \\m(...TRUNCATED) | "(Turkey TST 2013 P2)\n\nFind all functions $f: \\mathbb{R} \\rightarrow \\mathbb{R}_{+}^{*}$ such t(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | x^2 + x + 1 | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Find all functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R}_{+}^{*} \\) suc(...TRUNCATED) | [
false
] | [
"f(x) = x^2 + 1"
] | rephrase | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer by rechecking the steps provided in the model response.\n\n1. Substituti(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given a complex number $z\\left(2+i\\right)=2-i$, where $i$ is the imaginar(...TRUNCATED) | Given a complex number $z\left(2+i\right)=2-i$, where $i$ is the imaginary unit, find $|z|$. | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 1 | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Find \\( |z| \\) given \\( z(2+i) = 2-i \\).\n\nStep 1: Solve for \\( z \\).\n(...TRUNCATED) | [
true
] | [
"1"
] | rephrase | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer by checking each step of the solution provided.\n\n1. The initial setup (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given a complex number $z\\left(2+i\\right)=2-i$, where $i$ is the imaginar(...TRUNCATED) | Given a complex number $z\left(2+i\right)=2-i$, where $i$ is the imaginary unit, find $|z|$. | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 1 | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Find \\( |z| \\) given \\( z(2+i) = 2-i \\).\n\nStep 1: Solve for \\( z \\).\n(...TRUNCATED) | [
true
] | [
"1"
] | rephrase | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer by checking each step:\n\n1. Solving for \\( z \\):\n \\[\n z = \\fr(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given a complex number $z\\left(2+i\\right)=2-i$, where $i$ is the imaginar(...TRUNCATED) | Given a complex number $z\left(2+i\right)=2-i$, where $i$ is the imaginary unit, find $|z|$. | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 1 | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To solve for \\( |z| \\) given that \\( z(2 + i) = 2 - i \\), we first need to isolate \\( z \\).\(...TRUNCATED) | [
true
] | [
"1"
] | alternative | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer by checking the calculations and logic provided in the model response.\n(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given a complex number $z\\left(2+i\\right)=2-i$, where $i$ is the imaginar(...TRUNCATED) | Given a complex number $z\left(2+i\right)=2-i$, where $i$ is the imaginary unit, find $|z|$. | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 1 | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To find \\( |z| \\) given that \\( z(2+i) = 2-i \\), we can follow these steps:\n\n1. **Isolate \\(...TRUNCATED) | [
true
] | [
"1"
] | alternative | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer by checking the steps provided in the model response. The model correctl(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
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