messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Please solve the equation presented here. 568x + 501 = -558"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 568x + 501 = -558 $\n\nMove all terms to the left (standard form):\n$ 568x + 1059 = 0 $\n\nIsolate the $x$ term:\n$ 568x = -1059 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 200
} |
[
{
"role": "user",
"content": "Can you compute this equation? Evaluate: ((6 + 200/4) * 8) + 5^5 - log_8(512) + (-378 mod 19) + floor(-78/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((6 + 200/4) * 8) + 5^5 - log_8(512) + (-378 mod 19) + floor(-78/2) $\n\nCompute each comp... | {
"type": "arithmetic",
"seed": 1337,
"index": 201
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 16x^2 + 142x + 169 = -164"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 16x^2 + 142x + 169 = -164 $\n\nMove all terms to the left (standard form):\n$ 16x^2 + 142x + 333 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 202
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{... | {
"type": "optimization",
"seed": 1337,
"index": 203
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Prove that $f(x,y)=\\frac12(3x^2+2y^2)+-5x+-4y+4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(3x^2+2y^2)+-5x+-4y+4 $\n\n$ \\frac{\\partial^2 f}{... | {
"type": "optimization",
"seed": 1337,
"index": 204
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. 8x - 12 - 166 = 42x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 8x - 12 - 166 = 42x^2 $\n\nMove all terms to the left (standard form):\n$ -42x^2 + 8x + -178 = 0 $\n\nApply the quadratic formula:\n$ x = \\fra... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 205
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Prove that $f(x)=7x^2+4x+-9$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=7x^2+4x+-9$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) ... | {
"type": "optimization",
"seed": 1337,
"index": 206
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Evaluate: ((-129 + -624/24) * 9) + 8^4 - log_2(4) + (-408 mod 5) + ceil(169/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-129 + -624/24) * 9) + 8^4 - log_2(4) + (-408 mod 5) + ceil(169/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 207
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Solve for $x$ (in radians): cos(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = 1 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(1) = 0 $\n\nThe ge... | {
"type": "trigonometry",
"seed": 1337,
"index": 208
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Prove that $f(x)=1x^2+-6x+-1$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=1x^2+-6x+-1$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f... | {
"type": "optimization",
"seed": 1337,
"index": 209
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Solve for $x$ (in radians): sin(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 210
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Compute $(54+135) \\bmod 17$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (54+135) \\bmod 17 $\n\nUse the rule that addition is compatible with reduction modulo... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 211
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&4&-5\\\\\\-1&2&5\\\\\\5&1&0\\end{pmatrix},\\quad b=\\begin{pmatrix}2\\\\\\16\\\\\\-11\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=... | {
"type": "linear_algebra",
"seed": 1337,
"index": 212
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Compute the determinant: $A=\\begin{pmatrix}-8&-6\\\\2&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-8&-6\\\\\\2&2\\end{pmatrix} $\n\nUse $\\d... | {
"type": "linear_algebra",
"seed": 1337,
"index": 213
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Compute the indefinite integral: $\\int (-6x + -2)\\sin(5x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-6x + -2)\\sin(5x)\\,dx $\n\nUse standard antiderivatives (and integr... | {
"type": "calculus",
"seed": 1337,
"index": 214
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. 831 - 781 = -482x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 831 - 781 = -482x $\n\nMove all terms to the left (standard form):\n$ 482x + 50 = 0 $\n\nIsolate the $x$ term:\n$ 482x = -50 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 215
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Solve for $x$ (in radians): sin(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = 1 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(1) = 1.5708 $\n\nThe general solutions for $\\sin... | {
"type": "trigonometry",
"seed": 1337,
"index": 216
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Evaluate: ((-171 + 141/3) * 2) + 4^3 - log_2(16) + (-172 mod 22) + round(89/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-171 + 141/3) * 2) + 4^3 - log_2(16) + (-172 mod 22) + round(89/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 217
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Prove that $f(x,y)=\\frac12(4x^2+4y^2)+-6x+-6y+6$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(4x^2+4y^2)+-6x+-6y+6 $\n\n$ \\frac{\\partial^2 f}{\\pa... | {
"type": "optimization",
"seed": 1337,
"index": 218
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. 265 + 33x = 428"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 265 + 33x = 428 $\n\nMove all terms to the left (standard form):\n$ 33x + -163 = 0 $\n\nIsolate the $x$ term:\n$ 33x = 163 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 219
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. -40 - 25 + 28x = -171x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -40 - 25 + 28x = -171x^2 $\n\nMove all terms to the left (standard form):\n$ 171x^2 + 28x + -65 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 220
} |
[
{
"role": "user",
"content": "Please solve this math problem. -20x^2 - 40x + 106 = -115"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -20x^2 - 40x + 106 = -115 $\n\nMove all terms to the left (standard form):\n$ -20x^2 + -40x + 221 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 221
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Evaluate: ((23 + -512/16) * 18) + 11^2 - log_6(6) + (387 mod 15) + ceil(129/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((23 + -512/16) * 18) + 11^2 - log_6(6) + (387 mod 15) + ceil(129/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 222
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Compute the indefinite integral: $\\int (4x + 2)e^{6x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (4x + 2)e^{6x}\\,dx $\n\nUse standard antiderivatives (and integration by parts... | {
"type": "calculus",
"seed": 1337,
"index": 223
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Evaluate: ((56 + -893/19) * 11) + 2^2 - log_5(3125) + (-244 mod 19) + round(149/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((56 + -893/19) * 11) + 2^2 - log_5(3125) + (-244 mod 19) + round(1... | {
"type": "arithmetic",
"seed": 1337,
"index": 224
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. -10x - 69 + 100 = -80x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -10x - 69 + 100 = -80x^2 $\n\nMove all terms to the left (standard form):\n$ 80x^2 + -10x + 31 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 225
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. -17x + 27x^2 + 150 = 176"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -17x + 27x^2 + 150 = 176 $\n\nMove all terms to the left (standard form):\n$ 27x^2 + -17x + -26 = 0 $\n\nApply the quadrati... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 226
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, henc... | {
"type": "optimization",
"seed": 1337,
"index": 227
} |
[
{
"role": "user",
"content": "Solve the following math equation. Solve for $x$ (in radians): cos(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = 1 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(1) = 0 $\n\nThe general soluti... | {
"type": "trigonometry",
"seed": 1337,
"index": 228
} |
[
{
"role": "user",
"content": "Evaluate the following equation. -11 - 151x - 199 = 46x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -11 - 151x - 199 = 46x^2 $\n\nMove all terms to the left (standard form):\n$ -46x^2 + -151x + -210 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 229
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 230
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}2&-4&0\\\\\\1&4&2\\\\\\1&0&5\\end{pmatrix},\\quad b=\\begin{pmatrix}16\\\\\\-6\\\\\\-1\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 231
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Prove that $f(x,y)=\\frac12(7x^2+10y^2)+-6x+-6y+-7$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(7x^2+10y^2)+-6x+-6y+-7 $\n\n$ \\frac{\... | {
"type": "optimization",
"seed": 1337,
"index": 232
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Find the modular inverse of 29 modulo 36, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $29\\cdot a^{-1} \\equiv 1 \\pmod{36}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees i... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 233
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Compute the indefinite integral: $\\int -6\\sin(7x) + 7\\cos(6x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -6\\sin(7x) + 7\\cos(6x)\\,dx $\n\nUse standard antiderivatives... | {
"type": "calculus",
"seed": 1337,
"index": 234
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4... | {
"type": "optimization",
"seed": 1337,
"index": 235
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Evaluate: ((-199 + 48/2) * 4) + 11^3 - log_7(16807) + (394 mod 22) + ceil(1/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-199 + 48/2) * 4) + 11^3 - log_7(16807) + (394 mod 22) + ceil(1/2) $\n\nCompute each ... | {
"type": "arithmetic",
"seed": 1337,
"index": 236
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. 43x - 509 = -770"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 43x - 509 = -770 $\n\nMove all terms to the left (standard form):\n$ 43x + 261 = 0 $\n\nIsolate the $x$ term:\n$ 43x = -261 $\n\nDivide both sides by th... | {
"type": "linear_equation",
"seed": 1337,
"index": 237
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Compute $(-133+-167) \\bmod 8$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-133+-167) \\bmod 8 $\n\nUse the rule that addition is compatible with reduction m... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 238
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. 278 + 566 = -173x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 278 + 566 = -173x $\n\nMove all terms to the left (standard form):\n$ 173x + 844 = 0 $\n\nIsolate the $x$ term:\n$ 173x = -844 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 239
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-1&-1&-4\\\\\\-5&0&-4\\\\\\-4&-3&-1\\end{pmatrix},\\quad b=\\begin{pmatrix}10\\\\\\18\\\\\\10\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 240
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 877 + 822x = 547"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 877 + 822x = 547 $\n\nMove all terms to the left (standard form):\n$ 822x + 330 = 0 $\n\nIsolate the $x$ term:\n$ 822x = -330 $\n\nDivide both sides by the ... | {
"type": "linear_equation",
"seed": 1337,
"index": 241
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&0&3\\\\\\3&4&2\\\\\\-2&3&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}-18\\\\\\-3\\\\\\21\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve... | {
"type": "linear_algebra",
"seed": 1337,
"index": 242
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. -23x + 18x^2 - 37 = -142"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -23x + 18x^2 - 37 = -142 $\n\nMove all terms to the left (standard form):\n$ 18x^2 + -23x + 105 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 243
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Differentiate with respect to $x$: $f(x) = \\ln(3x + 4)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(3x + 4) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{3}{3x ... | {
"type": "calculus",
"seed": 1337,
"index": 244
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. 26 + 172x - 140 = 42x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 26 + 172x - 140 = 42x^2 $\n\nMove all terms to the left (standard form):\n$ -42x^2 + 172x + -114 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 245
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Solve for $x$ (in radians): cos(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arcco... | {
"type": "trigonometry",
"seed": 1337,
"index": 246
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. 966x - 894 = 327"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 966x - 894 = 327 $\n\nMove all terms to the left (standard form):\n$ 966x + -1221 = 0 $\n\nIsolate the $x$ term:\n$ 966x = 1221 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 247
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. 283 - 686x = -194"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 283 - 686x = -194 $\n\nMove all terms to the left (standard form):\n$ -686x + 477 = 0 $\n\nIsolate the $x$ term:\n$ -686x = -477 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 248
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Solve for $x$ (in radians): sin(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = 0 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(0) = 0 $\n\nThe general ... | {
"type": "trigonometry",
"seed": 1337,
"index": 249
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Compute the indefinite integral: $\\int 7\\sin(3x) + -5\\cos(2x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 7\\sin(3x) + -5\\cos(2x)\\,dx $\n\nUse standard antiderivatives (a... | {
"type": "calculus",
"seed": 1337,
"index": 250
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. 27 - 93x - 28 = -89x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 27 - 93x - 28 = -89x^2 $\n\nMove all terms to the left (standard form):\n$ 89x^2 + -93x + -1 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 251
} |
[
{
"role": "user",
"content": "solve: \n\n Compute the indefinite integral: $\\int 3x^3 + -4x^2 + 12x + -15\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3x^3 + -4x^2 + 12x + -15\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):... | {
"type": "calculus",
"seed": 1337,
"index": 252
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Evaluate: ((191 + 24/4) * 7) + 3^3 - log_8(32768) + (428 mod 20) + floor(12/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((191 + 24/4) * 7) + 3^3 - log_8(32768) + (428 mod 20) + floor(12/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 253
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Evaluate: ((-134 + 39/3) * 1) + 3^2 - log_3(9) + (-127 mod 18) + round(52/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-134 + 39/3) * 1) + 3^2 - log_3(9) + (-127 mod 18) + round(52/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 254
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Evaluate: ((27 + -132/12) * 5) + 10^4 - log_4(4096) + (284 mod 10) + round(135/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((27 + -132/12) * 5) + 10^4 - log_4(4096) + (284 mod 10) + round(135/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 255
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Evaluate: ((-174 + 240/5) * 19) + 6^5 - log_6(6) + (-7 mod 4) + round(180/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-174 + 240/5) * 19) + 6^5 - log_6(6) + (-7 mod 4) + round(180/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 256
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 29 - 79x - 159 = -32x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 29 - 79x - 159 = -32x^2 $\n\nMove all terms to the left (standard form):\n$ 32x^2 + -79x + -130 = 0 $\n\nApply the quadratic formula:\n$ x = \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 257
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. -421 - 715 = 739x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -421 - 715 = 739x $\n\nMove all terms to the left (standard form):\n$ -739x + -1136 = 0 $\n\nIsolate the $x$ term:\n$ -739x = 1136 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 258
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. -87x - 551 = 214"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -87x - 551 = 214 $\n\nMove all terms to the left (standard form):\n$ -87x + -765 = 0 $\n\nIsolate the $x$ term:\n$ -87x = 765 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 259
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n... | {
"type": "trigonometry",
"seed": 1337,
"index": 260
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Compute $(-104+-132) \\bmod 10$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-104+-132) \\bmod 10 $\n\nUse the rule that addition is compatible with reduct... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 261
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. -232 - 875 = 546x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -232 - 875 = 546x $\n\nMove all terms to the left (standard form):\n$ -546x + -1107 = 0 $\n\nIsolate the $x$ term:\n$ -546x = 1107 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 262
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-8&4\\\\7&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -8 & 4 \\\\ 7 & 1 \\end{pmatrix} $\n\nComp... | {
"type": "linear_algebra",
"seed": 1337,
"index": 263
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Evaluate: ((160 + -288/8) * 1) + 9^4 - log_8(262144) + (419 mod 27) + floor(117/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((160 + -288/8) * 1) + 9^4 - log_8(262144) + (419 mod 27) + floor(117/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 264
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Compute $(-8+103) \\bmod 20$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-8+103) \\bmod 20 $\n\nUse the rule that addition is compatible with reduction modul... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 265
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. -988 - 875x = 547"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -988 - 875x = 547 $\n\nMove all terms to the left (standard form):\n$ -875x + -1535 = 0 $\n\nIsolate the $x$ term:\n$ -875x = 1535 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 266
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Compute the indefinite integral: $\\int 9\\sin(5x) + -2\\cos(7x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 9\\sin(5x) + -2\\cos(7x)\\,dx $\n\nUse standard antiderivatives (and... | {
"type": "calculus",
"seed": 1337,
"index": 267
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. -8 + 60 - 84x^2 = 124x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -8 + 60 - 84x^2 = 124x $\n\nMove all terms to the left (standard form):\n$ -84x^2 + -124x + 52 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 268
} |
[
{
"role": "user",
"content": "Please calculate this equation. Evaluate: ((44 + -75/5) * 18) + 4^2 - log_8(4096) + (247 mod 24) + floor(101/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((44 + -75/5) * 18) + 4^2 - log_8(4096) + (247 mod 24) + floor(101/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 269
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. 31x - 174 - 77x^2 = 107"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 31x - 174 - 77x^2 = 107 $\n\nMove all terms to the left (standard form):\n$ -77x^2 + 31x + -281 = 0 $\n\nApply the quadratic ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 270
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x... | {
"type": "optimization",
"seed": 1337,
"index": 271
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Differentiate with respect to $x$: $f(x) = -4x^3 + 2x^2 + -18x + 11$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -4x^3 + 2x^2 + -18x + 11 $\n\nApply the standard differentiation r... | {
"type": "calculus",
"seed": 1337,
"index": 272
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}0&6\\\\\\4&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}-48\\\\\\40\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}0&6\\\\\\4&-2\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 273
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Prove that $f(x)=9x^2+1x+-1$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+1x+-1$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x... | {
"type": "optimization",
"seed": 1337,
"index": 274
} |
[
{
"role": "user",
"content": "solve Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-6&-5\\\\\\6&-7\\end{pmatrix},\\quad b=\\begin{pmatrix}44\\\\\\-68\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-6&-5\\\\\\6&-7\\end{pmatrix} ,\\quad b=\\begin{pm... | {
"type": "linear_algebra",
"seed": 1337,
"index": 275
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. -840 + 735x = 407"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -840 + 735x = 407 $\n\nMove all terms to the left (standard form):\n$ 735x + -1247 = 0 $\n\nIsolate the $x$ term:\n$ 735x = 1247 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 276
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. 843x - 96 = -867"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 843x - 96 = -867 $\n\nMove all terms to the left (standard form):\n$ 843x + 771 = 0 $\n\nIsolate the $x$ term:\n$ 843x = -771 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 277
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Find the modular inverse of 23 modulo 40, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $23\\cdot a^{-1} \\equiv 1 \\pmod{40}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 278
} |
[
{
"role": "user",
"content": "Please solve this math problem. Evaluate: ((-20 + 748/22) * 1) + 3^4 - log_7(2401) + (-162 mod 17) + ceil(48/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-20 + 748/22) * 1) + 3^4 - log_7(2401) + (-162 mod 17) + ceil(48/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 279
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Differentiate with respect to $x$: $f(x) = 2x^3 + -5x^2 + 10x + -16$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2x^3 + -5x^2 + 10x + -16 $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 280
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((84 + -190/10) * 15) + 6^2 - log_8(32768) + (-199 mod 30) + ceil(141/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((84 + -190/10) * 15) + 6^2 - log_8(32768) + (-199 mod 30) + ceil(141/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 281
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, he... | {
"type": "optimization",
"seed": 1337,
"index": 282
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=... | {
"type": "optimization",
"seed": 1337,
"index": 283
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Evaluate: ((67 + 370/10) * 3) + 5^5 - log_4(16) + (-385 mod 22) + floor(-153/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((67 + 370/10) * 3) + 5^5 - log_4(16) + (-385 mod 22) + floor(-153/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 284
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4x(x^2-1... | {
"type": "optimization",
"seed": 1337,
"index": 285
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Compute the indefinite integral: $\\int \\ln(1x + 8)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(1x + 8)\\,dx $\n\nUse standard antiderivatives (and integration by parts if need... | {
"type": "calculus",
"seed": 1337,
"index": 286
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. 27x^2 - 187 - 168x = -3"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 27x^2 - 187 - 168x = -3 $\n\nMove all terms to the left (standard form):\n$ 27x^2 + -168x + -184 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 287
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Solve for $x$ (in radians): cos(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal va... | {
"type": "trigonometry",
"seed": 1337,
"index": 288
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Evaluate: ((146 + 22/2) * 10) + 8^2 - log_5(125) + (27 mod 20) + floor(175/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((146 + 22/2) * 10) + 8^2 - log_5(125) + (27 mod 20) + floor(175/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 289
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Evaluate: ((124 + 180/15) * 12) + 5^3 - log_10(100) + (-443 mod 26) + ceil(-74/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((124 + 180/15) * 12) + 5^3 - log_10(100) + (-443 mod 26) + cei... | {
"type": "arithmetic",
"seed": 1337,
"index": 290
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. -470 + 744 = 982x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -470 + 744 = 982x $\n\nMove all terms to the left (standard form):\n$ -982x + 274 = 0 $\n\nIsolate the $x$ term:\n$ -982x = -274 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 291
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\partial^2 f}{... | {
"type": "optimization",
"seed": 1337,
"index": 292
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. -40 - 57x + 176 = -118x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -40 - 57x + 176 = -118x^2 $\n\nMove all terms to the left (standard form):\n$ 118x^2 + -57x + 136 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 293
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Compute the indefinite integral: $\\int 8e^{1x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 8e^{1x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\... | {
"type": "calculus",
"seed": 1337,
"index": 294
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Compute the determinant: $A=\\begin{pmatrix}-5&9\\\\3&-7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-5&9\\\\\\3&-7\\end{pmatrix} $\n\nUs... | {
"type": "linear_algebra",
"seed": 1337,
"index": 295
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Evaluate: ((89 + -350/10) * 10) + 9^2 - log_8(4096) + (-423 mod 11) + ceil(-85/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((89 + -350/10) * 10) + 9^2 - log_8(4096) + (-423 mod 11) + ceil(-85/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 296
} |
[
{
"role": "user",
"content": "Work out the result of this equation. -42 - 186 - 98x = 166x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -42 - 186 - 98x = 166x^2 $\n\nMove all terms to the left (standard form):\n$ -166x^2 + -98x + -228 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 297
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Solve for $x$ (in radians): sin(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = 0 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(0) = 0 $\n\nThe gene... | {
"type": "trigonometry",
"seed": 1337,
"index": 298
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-6&2\\\\0&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -6 & 2 \\\\ 0 & 1 \\end{pmatrix} $\n\nCompute t... | {
"type": "linear_algebra",
"seed": 1337,
"index": 299
} |
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