uuid string | expected_answer string | problem string | original_expected_answer string | changed_answer_to_majority bool | data_source string | messages list | used_in list | metadata dict | license string | tools list | url string | user_name string | user_url string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\displaystyle
\frac{2c_{1}}{c_{2}}
\big(e^{c_{2}(\phi_{1}+c_{3})}
-e^{c_{2}(\phi_{0}+c_{3})}\big)
-\frac{2c_{1}}{c_{4}}
\big(e^{c_{4}(\phi_{1}+c_{3})}
-e^{c_{4}(\phi_{0}+c_{3})}\big)=1 | Find a symbolic closed-form solution to the boundary value problem (BVP) given by the differential equation
$$\frac{d^2 \phi}{dx^2} = c_1 \left ( e^{c_2(\phi(x)+c_3)} - e^{c_4(\phi(x)+c_3)} \right )$$
with boundary conditions $\phi'(0) = 0$ and $\phi'(1) = 1$ in the domain $(0,1)$, where $c_1, c_2, c_3,$ and $c_4$ ar... | null | true | stackflow | [
{
"role": "system",
"content": "Reasoning: high",
"reasoning_content": "",
"tool_calls": [],
"tool_call_id": "",
"name": ""
},
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind a symbolic closed... | [] | {
"reason_low_with_tool": {
"count": 8,
"pass": 0,
"accuracy": 0
},
"reason_low_no_tool": {
"count": 8,
"pass": 0,
"accuracy": 0
},
"reason_medium_with_tool": {
"count": 8,
"pass": 0,
"accuracy": 0
},
"reason_medium_no_tool": {
"count": 8,
"pass": 1,
"accura... | cc-by-sa-4.0 | [] | https://math.stackexchange.com/questions/1899965/analytical-closed-form-solution-to-a-2nd-order-bvp-with-two-derivative-bcs | Dr Krishnakumar Gopalakrishnan | https://math.stackexchange.com/users/253523/dr-krishnakumar-gopalakrishnan | |
\,f(x)=(x^{4}-10x^{2}+1)\;(x^{3}-3x-1)\;(x^{5}+x^{4}-4x^{3}-3x^{2}+3x+1)\, | Is there a solvable polynomial whose Galois group has order 60? If it exists, provide an example. | \( x^{15} - 30x^{10} - 3708x^5 - 2 \) | true | stackflow | [
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIs there a solvable polynomial whose Galois group has order 60? If it exists, provide an example.",
"reasoning_content": "",
"tool_calls": [],
"tool_call_id": "",
... | [
"nano_v3"
] | {
"reason_low_with_tool": {
"count": 8,
"pass": 0,
"accuracy": 0
},
"reason_low_no_tool": {
"count": 8,
"pass": 0,
"accuracy": 0
},
"reason_medium_with_tool": {
"count": 8,
"pass": 0,
"accuracy": 0
},
"reason_medium_no_tool": {
"count": 8,
"pass": 0,
"accura... | cc-by-sa-4.0 | [] | https://math.stackexchange.com/questions/4454833/how-to-get-a-polynomial-corresponding-to-a-solvable-galois-group-of-order-60 | mayi | https://math.stackexchange.com/users/332197/mayi | |
\(\theta \in [0, \frac{\pi}{2}], \quad \phi \in [0, \frac{\pi}{2}]\) | Evaluate the triple integral \(\iiint_V (x^2 + y^2) \, dx \, dy \, dz\) where \(V\) is the region in the positive octant bounded by the sphere \(r = a\). Determine the appropriate limits for \(\theta\) and \(\phi\) in spherical coordinates. | \(\theta \in [0, \frac{\pi}{2}], \quad \phi \in [0, \frac{\pi}{2}]\) | false | stackflow | [
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nEvaluate the triple integral \\(\\iiint_V (x^2 + y^2) \\, dx \\, dy \\, dz\\) where \\(V\\) is the region in the positive octant bounded by the sphere \\(r = a\\). Determine the... | [
"nano_v3"
] | {
"reason_low_with_tool": {
"count": 8,
"pass": 4,
"accuracy": 0.5
},
"reason_low_no_tool": {
"count": 8,
"pass": 2,
"accuracy": 0.25
},
"reason_medium_with_tool": {
"count": 8,
"pass": 3,
"accuracy": 0.375
},
"reason_medium_no_tool": {
"count": 8,
"pass": 4,
... | cc-by-sa-4.0 | [] | https://math.stackexchange.com/questions/745224/triple-integration-in-the-positive-ocatant | Sammy | https://math.stackexchange.com/users/141654/sammy | |
"\\;\nu_{n}\n =\\sum_{k=0}^{\\lfloor n/10\\rfloor}\n \\Bigl(\\sum_{m=0}^{\\,n-10k}p_{2}(m)\\B(...TRUNCATED) | "Given the sequence defined by:\n\\[ u_0 = 1, \\]\n\\[ u_1 = 1, \\]\n\\[ u_n = u_{n-1} + u_{\\lfloor(...TRUNCATED) | null | true | stackflow | [{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | [
"nano_v3"
] | {"reason_low_with_tool":{"count":8,"pass":0,"accuracy":0.0},"reason_low_no_tool":{"count":8,"pass":0(...TRUNCATED) | cc-by-sa-4.0 | [] | https://math.stackexchange.com/questions/3379408/closed-form-for-recurrence-sequences | suho | https://math.stackexchange.com/users/710975/suho | |
\( q \neq 0 \) | "For which values of the coefficient \\( q \\) does the Diophantine equation \\( X^2 + Y^2 = qZ^3 \\(...TRUNCATED) | \( q \neq 0 \) | false | stackflow | [{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | [
"nano_v3"
] | {"reason_low_with_tool":{"count":8,"pass":5,"accuracy":0.625},"reason_low_no_tool":{"count":8,"pass"(...TRUNCATED) | cc-by-sa-4.0 | [] | https://mathoverflow.net/questions/180914/diophantine-equation | FisiaiLusia | https://mathoverflow.net/users/54245/fisiailusia | |
"\\displaystyle \n\\sum_{n=1}^{\\infty}\\frac{1}{\\sqrt n}\\arctan\\frac{1}{n\\sqrt n}\n= \\frac{245(...TRUNCATED) | "Evaluate the series \\(\\sum_{n=1}^{\\infty} \\frac{1}{\\sqrt{n}} \\arctan \\frac{1}{n \\sqrt{n}}\\(...TRUNCATED) | null | true | stackflow | [{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | [
"nano_v3"
] | {"reason_low_with_tool":{"count":8,"pass":0,"accuracy":0.0},"reason_low_no_tool":{"count":8,"pass":0(...TRUNCATED) | cc-by-sa-4.0 | [] | https://math.stackexchange.com/questions/2102984/an-arctan-series-with-roots-sum-n-1-infty-frac-1-sqrt-n-arctan-frac-1-n-sqrt-n | Tolaso | https://math.stackexchange.com/users/203035/tolaso | |
"\\;\n\\begin{aligned}\nC(\\beta)=\\frac{\\cos(\\pi\\beta/2)}{1-\\beta}\n&+\\frac{\\cos(\\pi\\beta/2(...TRUNCATED) | "Find the closed form of the integral \\( C(\\beta) = \\int_0^\\frac{\\pi}{2} \\frac{\\cos(\\theta)}(...TRUNCATED) | null | true | stackflow | [{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | [
"nano_v3"
] | {"reason_low_with_tool":{"count":8,"pass":0,"accuracy":0.0},"reason_low_no_tool":{"count":8,"pass":0(...TRUNCATED) | cc-by-sa-4.0 | [] | https://math.stackexchange.com/questions/2974867/closed-forms-of-int-0-frac-pi-2-frac-sin-alpha-phi-sin-phi-d-phi-and-int-0-frac- | aleden | https://math.stackexchange.com/users/468742/aleden | |
2f=a^{2}-v^{2}-w^{2} | How to diagonalize the quadratic form $f(x,y,z) = xy + yz + xz$? | \( u^2 - \frac{1}{4}v^2 - w^2 \) | true | stackflow | [{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | [
"nano_v3"
] | {"reason_low_with_tool":{"count":8,"pass":0,"accuracy":0.0},"reason_low_no_tool":{"count":8,"pass":0(...TRUNCATED) | cc-by-sa-4.0 | [] | https://math.stackexchange.com/questions/422601/how-to-diagonalize-f-x-y-z-xy-yz-xz | Hagrid | https://math.stackexchange.com/users/57139/hagrid | |
"Evaluate the integral\n\\[ \\int_0^1 \\frac{x^4}{\\max(x(P_{1y} - P_{2y}) + P_{2y} - w, 0) + h} \\,(...TRUNCATED) | null | true | stackflow | [{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | [
"nano_v3"
] | {"reason_low_with_tool":{"count":8,"pass":0,"accuracy":0.0},"reason_low_no_tool":{"count":7,"pass":0(...TRUNCATED) | cc-by-sa-4.0 | [] | https://math.stackexchange.com/questions/3066923/integrating-with-a-max-function-as-denominator | Wicpar | https://math.stackexchange.com/users/203298/wicpar | ||
"\n\\begin{array}{l}\n\\text{If the percentages are rounded to two decimals: }\\\\\n\\qquad N\\in\\{(...TRUNCATED) | "Given the percentage results of a quiz with non-uniform percentages, determine all possible numbers(...TRUNCATED) | null | true | stackflow | [{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | [
"nano_v3"
] | {"reason_low_with_tool":{"count":8,"pass":1,"accuracy":0.125},"reason_low_no_tool":{"count":8,"pass"(...TRUNCATED) | cc-by-sa-4.0 | [] | https://math.stackexchange.com/questions/2795478/find-all-possible-solutions-to-how-many-people-voted-on-a-quiz | johndb | https://math.stackexchange.com/users/564868/johndb |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 28