conversations listlengths 2 2 | question stringlengths 33 2.02k | source null | id null | prompt listlengths 2 2 | answer stringclasses 491
values | prompt__example_annotation__metadata dict | task_source stringclasses 1
value | task_config stringclasses 1
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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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[
{
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"value": "10. The number of integer solutions to the inequality $\\log _{6}(1+\\sqrt{x})>\\log _{25} x$ is $\\qquad$ ."
},
{
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"value": "<think>\nOkay, let's tackle this problem step by step. The question is about finding the number of integer solutions to th... | 10. The number of integer solutions to the inequality $\log _{6}(1+\sqrt{x})>\log _{25} x$ is $\qquad$ . | 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... | 24 | {
"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 | [
"Rewritten Question: Find the number of integer solutions to the inequality $\\log_{6}(1+\\sqrt{x}) > \\log_{25} x$.\n\nTo solve this problem, we need to analyze the given inequality step by step:\n\nStep 1: Rewrite the inequality using properties of logarithms.\nSince $\\log_{25} x = \\frac{\\log_{6} x}{\\log_{6} ... | [
true
] | [
"24"
] | rephrase_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. Rewriting the question as \"Find the number of integer solutions to the inequality $\\log_{6}(1+\\sqrt{x}) > \\log_{25} x$\" and following the steps closely mirrors the solution path taken in the model response. The key transformations and comparisons were correctly outlined, including t... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.218:9080/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":"10. The number of integer solutions to the inequality $\\log _{6}(1+\\sqrt{(...TRUNCATED) | "10. The number of integer solutions to the inequality $\\log _{6}(1+\\sqrt{x})>\\log _{25} x$ is $\(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 24 | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Firstly, let's analyze the given inequality \\(\\log_{6}(1 + \\sqrt{x}) > \\log_{25} x\\).\n\n### (...TRUNCATED) | [
true
] | [
"24"
] | alternative_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 analyzed the inequality \\(\\log_{6}(1 + \(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/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":"10. The number of integer solutions to the inequality $\\log _{6}(1+\\sqrt{(...TRUNCATED) | "10. The number of integer solutions to the inequality $\\log _{6}(1+\\sqrt{x})>\\log _{25} x$ is $\(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 24 | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Firstly, let's consider the domain restrictions of both logarithmic functions involved. For \\(\\l(...TRUNCATED) | [
true
] | [
"24"
] | alternative_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer by re-evaluating the model's logic and calculations.\n\nThe model correc(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/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":"The domain of the function $f\\left(x\\right)=\\sqrt{x-2}+\\sqrt{3-x}$ is _(...TRUNCATED) | The domain of the function $f\left(x\right)=\sqrt{x-2}+\sqrt{3-x}$ is ____. | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | [2, 3] | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Find the domain of the function \\( f(x) = \\sqrt{x-2} + \\sqrt{3-x} \\).\n\nT(...TRUNCATED) | [
true
] | [
"[2, 3]"
] | rephrase_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 the domain constraints for each square r(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/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":"The domain of the function $f\\left(x\\right)=\\sqrt{x-2}+\\sqrt{3-x}$ is _(...TRUNCATED) | The domain of the function $f\left(x\right)=\sqrt{x-2}+\sqrt{3-x}$ is ____. | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | [2, 3] | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Find the domain of the function \\( f(x) = \\sqrt{x-2} + \\sqrt{3-x} \\).\n\nT(...TRUNCATED) | [
true
] | [
"[2, 3]"
] | rephrase_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 the conditions for the domain by ensurin(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/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":"The domain of the function $f\\left(x\\right)=\\sqrt{x-2}+\\sqrt{3-x}$ is _(...TRUNCATED) | The domain of the function $f\left(x\right)=\sqrt{x-2}+\sqrt{3-x}$ is ____. | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | [2, 3] | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To determine the domain of the function \\( f(x) = \\sqrt{x-2} + \\sqrt{3-x} \\), we need to ensur(...TRUNCATED) | [
true
] | [
"[2, 3]"
] | alternative_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 determined the domain by ensuring that both square (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/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":"The domain of the function $f\\left(x\\right)=\\sqrt{x-2}+\\sqrt{3-x}$ is _(...TRUNCATED) | The domain of the function $f\left(x\right)=\sqrt{x-2}+\sqrt{3-x}$ is ____. | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | [2, 3] | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To determine the domain of the function \\( f(x) = \\sqrt{x-2} + \\sqrt{3-x} \\), we need to ensur(...TRUNCATED) | [
true
] | [
"[2, 3]"
] | alternative_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 both \\( \\sqrt{x-2} \\) and \\( \\(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/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":"Integers from 1 to 100 are placed in a row in some order. Let us call a num(...TRUNCATED) | "Integers from 1 to 100 are placed in a row in some order. Let us call a number [i]large-right[/i], (...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 50 | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Integers from 1 to 100 are placed in a row. A number is called large-right if (...TRUNCATED) | [
true
] | [
"50"
] | rephrase_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 constructs a permutation where the first 50 numbers (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/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":"Integers from 1 to 100 are placed in a row in some order. Let us call a num(...TRUNCATED) | "Integers from 1 to 100 are placed in a row in some order. Let us call a number [i]large-right[/i], (...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 50 | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Integers from 1 to 100 are placed in a row. A number is called large-right if (...TRUNCATED) | [
true
] | [
"50"
] | rephrase_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 suggests that the maximal possible value of \\( k \\(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/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":"Integers from 1 to 100 are placed in a row in some order. Let us call a num(...TRUNCATED) | "Integers from 1 to 100 are placed in a row in some order. Let us call a number [i]large-right[/i], (...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 50 | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Integers from 1 to 100 are placed in a row in some order. A number is called l(...TRUNCATED) | [
true
] | [
"50"
] | rephrase_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 suggests that the maximal possible value of \\( k \\(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/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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