messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Calculate and solve this equation. Differentiate with respect to $x$: $f(x) = (-4x + -7)e^{6x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-4x + -7)e^{6x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-4e^{6x} ... | {
"type": "calculus",
"seed": 1337,
"index": 4200
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. 994 - 886 = 136x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 994 - 886 = 136x $\n\nMove all terms to the left (standard form):\n$ -136x + 108 = 0 $\n\nIsolate the $x$ term:\n$ -136x = -108 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 4201
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Evaluate: ((133 + -760/19) * 1) + 11^2 - log_10(1000000) + (458 mod 30) + round(-128/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((133 + -760/19) * 1) + 11^2 - log_10(1000000) + (458 mod 30) + round(-128/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 4202
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Evaluate: ((97 + -77/7) * 7) + 12^3 - log_6(216) + (114 mod 6) + floor(22/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((97 + -77/7) * 7) + 12^3 - log_6(216) + (114 mod 6) + floor(22/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 4203
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Find the modular inverse of 17 modulo 25, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $17\\cdot a^{-1} \\equiv 1 \\pmod{25}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4204
} |
[
{
"role": "user",
"content": "Solve this equation accurately. 135x - 823 = -639"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 135x - 823 = -639 $\n\nMove all terms to the left (standard form):\n$ 135x + -184 = 0 $\n\nIsolate the $x$ term:\n$ 135x = 184 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 4205
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Compute $(32+-20) \\bmod 13$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (32+-20) \\bmod 13 $\n\nUse the rule that addition is compatible with reduction m... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4206
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Evaluate: ((82 + -50/25) * 10) + 10^3 - log_4(64) + (-243 mod 8) + floor(16/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((82 + -50/25) * 10) + 10^3 - log_4(64) + (-243 mod 8) + floor(16/2) $\n\nCompute each co... | {
"type": "arithmetic",
"seed": 1337,
"index": 4207
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Evaluate: ((117 + 351/9) * 20) + 9^5 - log_6(1296) + (32 mod 2) + floor(148/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((117 + 351/9) * 20) + 9^5 - log_6(1296) + (32 mod 2) + floor(148/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 4208
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Evaluate: ((60 + -616/22) * 17) + 8^5 - log_7(16807) + (287 mod 5) + ceil(-190/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((60 + -616/22) * 17) + 8^5 - log_7(16807) + (287 mod 5) + ceil(-190/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 4209
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Compute the indefinite integral: $\\int (-3x + -6)\\sin(1x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-3x + -6)\\sin(1x)\\,dx $\n\nUse standard antiderivatives (and integration... | {
"type": "calculus",
"seed": 1337,
"index": 4210
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. -31x - 187 - 111x^2 = 151"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -31x - 187 - 111x^2 = 151 $\n\nMove all terms to the left (standard form):\n$ -111x^2 + -31x + -338 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4211
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Compute the indefinite integral: $\\int 1\\sin(3x) + 0\\cos(2x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 1\\sin(3x) + 0\\cos(2x)\\,dx $\n\nUse standard antiderivativ... | {
"type": "calculus",
"seed": 1337,
"index": 4212
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Evaluate: ((37 + -414/18) * 18) + 9^3 - log_9(9) + (146 mod 7) + floor(148/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((37 + -414/18) * 18) + 9^3 - log_9(9) + (146 mod 7) + floor(148/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 4213
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Evaluate: ((184 + -155/5) * 17) + 5^5 - log_9(59049) + (-48 mod 14) + floor(-20/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((184 + -155/5) * 17) + 5^5 - log_9(59049) + (-48 mod 14) + floor(-20/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4214
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Evaluate: ((174 + -470/10) * 19) + 6^2 - log_6(46656) + (-189 mod 17) + floor(69/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((174 + -470/10) * 19) + 6^2 - log_6(46656) + (-189 mod 17) + floor(69/... | {
"type": "arithmetic",
"seed": 1337,
"index": 4215
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-8&4\\\\\\-9&-8\\end{pmatrix},\\quad b=\\begin{pmatrix}-68\\\\\\-89\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-8&4\\\\\\-9&-8\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4216
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Prove that $f(x)=5x^2+-8x+8$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+-8x+8$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 10x + -8 $... | {
"type": "optimization",
"seed": 1337,
"index": 4217
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Compute the indefinite integral: $\\int -1\\sin(9x) + -8\\cos(6x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -1\\sin(9x) + -8\\cos(6x)\\,dx $\n\nUse standard antiderivatives... | {
"type": "calculus",
"seed": 1337,
"index": 4218
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Compute the indefinite integral: $\\int \\ln(9x + -1)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(9x + -1)\\,dx $\n\nUse standard antiderivatives (and integration by par... | {
"type": "calculus",
"seed": 1337,
"index": 4219
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Evaluate: ((-68 + 58/2) * 18) + 5^3 - log_5(125) + (-147 mod 15) + floor(-156/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-68 + 58/2) * 18) + 5^3 - log_5(125) + (-147 mod 15) + floor(-156/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4220
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Find the modular inverse of 26 modulo 27, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $26\\cdot a^{-1} \\equiv 1 \\pmod{27}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4221
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$... | {
"type": "trigonometry",
"seed": 1337,
"index": 4222
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. 467x + 431 = 31"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 467x + 431 = 31 $\n\nMove all terms to the left (standard form):\n$ 467x + 400 = 0 $\n\nIsolate the $x$ term:\n$ 467x = -400 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 4223
} |
[
{
"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": 4224
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}2&5\\\\\\-6&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}-41\\\\\\39\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}2&5... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4225
} |
[
{
"role": "user",
"content": "Solve the equation shown below. 403 - 136 = -185x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 403 - 136 = -185x $\n\nMove all terms to the left (standard form):\n$ 185x + 267 = 0 $\n\nIsolate the $x$ term:\n$ 185x = -267 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 4226
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. -34x^2 + 187 - 30x = -80"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -34x^2 + 187 - 30x = -80 $\n\nMove all terms to the left (standard form):\n$ -34x^2 + -30x + 267 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4227
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Solve for $x$ (in radians): sin(x) = \\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha... | {
"type": "trigonometry",
"seed": 1337,
"index": 4228
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Solve for $x$ (in radians): tan(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\ar... | {
"type": "trigonometry",
"seed": 1337,
"index": 4229
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Prove that $f(x,y)=\\frac12(5x^2+4y^2)+2x+3y+3$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(5x^2+4y^2)+2x+3y+3 $\n\n$ \\frac{\\partial^2 f}{... | {
"type": "optimization",
"seed": 1337,
"index": 4230
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. 26x - 58 + 153 = 69x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 26x - 58 + 153 = 69x^2 $\n\nMove all terms to the left (standard form):\n$ -69x^2 + 26x + 95 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4231
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. 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 = \\arccos... | {
"type": "trigonometry",
"seed": 1337,
"index": 4232
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. -28x + 155 - 41x^2 = -10"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -28x + 155 - 41x^2 = -10 $\n\nMove all terms to the left (standard form):\n$ -41x^2 + -28x + 165 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4233
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Compute the indefinite integral: $\\int \\ln(8x + -5)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(8x + -5)\\,dx $\n\nUse standard antiderivatives (and integration by part... | {
"type": "calculus",
"seed": 1337,
"index": 4234
} |
[
{
"role": "user",
"content": "Solve the following math equation. Compute the determinant: $A=\\begin{pmatrix}-6&-8\\\\-7&6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-6&-8\\\\\\-7&6\\end{pmatrix} $\n\nUse $\\det... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4235
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Prove that $f(x)=5x^2+-7x+4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+-7x+4$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 10... | {
"type": "optimization",
"seed": 1337,
"index": 4236
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}6&0\\\\2&-2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 6 & 0 \\\\ 2 & -2 \\end{pmatrix} $\n\nCompute the determinan... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4237
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. 211 + 308x = -411"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 211 + 308x = -411 $\n\nMove all terms to the left (standard form):\n$ 308x + 622 = 0 $\n\nIsolate the $x$ term:\n$ 308x = -622 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 4238
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-8&5\\\\\\-6&-8\\end{pmatrix},\\quad b=\\begin{pmatrix}-9\\\\\\-42\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-8&5\\\\\\-6&-8\\end{pma... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4239
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Evaluate: ((-65 + -940/20) * 5) + 3^4 - log_9(9) + (354 mod 22) + round(43/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-65 + -940/20) * 5) + 3^4 - log_9(9) + (354 mod 22) + round(43/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4240
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. 160 - 719 = -368x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 160 - 719 = -368x $\n\nMove all terms to the left (standard form):\n$ 368x + -559 = 0 $\n\nIsolate the $x$ term:\n$ 368x = 559 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4241
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. -635 - 662x = 38"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -635 - 662x = 38 $\n\nMove all terms to the left (standard form):\n$ -662x + -673 = 0 $\n\nIsolate the $x$ term:\n$ -662x = 673 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4242
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Compute the indefinite integral: $\\int 3e^{3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3e^{3x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\i... | {
"type": "calculus",
"seed": 1337,
"index": 4243
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. -534x - 896 = 505"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -534x - 896 = 505 $\n\nMove all terms to the left (standard form):\n$ -534x + -1401 = 0 $\n\nIsolate the $x$ term:\n$ -534x = 1401 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4244
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Compute $(66+-38) \\bmod 19$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (66+-38) \\bmod 19 $\n\nUse the rule that addition is compatible with reduction modulo $... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4245
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. 595x + 696 = 942"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 595x + 696 = 942 $\n\nMove all terms to the left (standard form):\n$ 595x + -246 = 0 $\n\nIsolate the $x$ term:\n$ 595x = 246 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 4246
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Compute $(189+186) \\bmod 19$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (189+186) \\bmod 19 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4247
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. -643 + 395x = 578"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -643 + 395x = 578 $\n\nMove all terms to the left (standard form):\n$ 395x + -1221 = 0 $\n\nIsolate the $x$ term:\n$ 395x = 1221 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 4248
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Evaluate: ((-181 + 663/17) * 5) + 5^4 - log_6(216) + (-421 mod 22) + floor(190/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-181 + 663/17) * 5) + 5^4 - log_6(216) + (-421 mod 22) + floor(190/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 4249
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(-\\frac{\... | {
"type": "trigonometry",
"seed": 1337,
"index": 4250
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Prove that $f(x,y)=\\frac12(9x^2+3y^2)+2x+-3y+1$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+3y^2)+2x+-3y+1 $\n\n$ \\frac{\\partial^2 f}{\\par... | {
"type": "optimization",
"seed": 1337,
"index": 4251
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. 19 - 160 + 73x^2 = 131x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 19 - 160 + 73x^2 = 131x $\n\nMove all terms to the left (standard form):\n$ 73x^2 + -131x + -141 = 0 $\n\nApply the quadratic... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4252
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Differentiate with respect to $x$: $f(x) = (2x + 10)\\sin(3x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (2x + 10)\\sin(3x) $\n\nApply the standard differentiation rules:\n$ f'(x) = ... | {
"type": "calculus",
"seed": 1337,
"index": 4253
} |
[
{
"role": "user",
"content": "Solve the following math equation. Evaluate: ((65 + -192/16) * 6) + 10^3 - log_8(512) + (-383 mod 25) + ceil(-46/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((65 + -192/16) * 6) + 10^3 - log_8(512) + (-383 mod 25) + ceil(-46/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 4254
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. 683 - 697 = -392x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 683 - 697 = -392x $\n\nMove all terms to the left (standard form):\n$ 392x + -14 = 0 $\n\nIsolate the $x$ term:\n$ 392x = 14 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 4255
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Evaluate: ((-15 + -133/19) * 14) + 7^5 - log_9(6561) + (-5 mod 29) + ceil(169/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-15 + -133/19) * 14) + 7^5 - log_9(6561) + (-5 mod 29) + ceil(169/2) $\n\nCompute each component:\n$... | {
"type": "arithmetic",
"seed": 1337,
"index": 4256
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. -50 + 82 + 137x = -137x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -50 + 82 + 137x = -137x^2 $\n\nMove all terms to the left (standard form):\n$ 137x^2 + 137x + 32 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4257
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Prove that $f(x)=9x^2+-7x+-6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+-7x+-6$.\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": 4258
} |
[
{
"role": "user",
"content": "Find the answer to 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 $f'(x)=0$, hence:... | {
"type": "optimization",
"seed": 1337,
"index": 4259
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Differentiate with respect to $x$: $f(x) = \\ln(5x + 6)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(5x + 6) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{5}{5x + 6}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 4260
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. -427 + 340 = 595x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -427 + 340 = 595x $\n\nMove all terms to the left (standard form):\n$ -595x + -87 = 0 $\n\nIsolate the $x$ term:\n$ -595x = 87 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4261
} |
[
{
"role": "user",
"content": "Please work out this equation. Differentiate with respect to $x$: $f(x) = (-1x + 9)e^{5x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-1x + 9)e^{5x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-1e^{5x} + (-1x... | {
"type": "calculus",
"seed": 1337,
"index": 4262
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. -29x - 166 - 98 = 124x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -29x - 166 - 98 = 124x^2 $\n\nMove all terms to the left (standard form):\n$ -124x^2 + -29x + -264 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4263
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Evaluate: ((83 + 296/8) * 11) + 12^4 - log_2(8) + (-143 mod 20) + ceil(61/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((83 + 296/8) * 11) + 12^4 - log_2(8) + (-143 mod 20) + ceil(61/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 4264
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Compute $(26+31) \\bmod 10$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (26+31) \\bmod 10 $\n\nUse the rule that addition is compatible with reduction mod... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4265
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}4&-8\\\\-5&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 4 & -8 \\\\ -5 & -8 \\end{pmatrix} $\n\nCompute... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4266
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. -50 + 19x - 48x^2 = 5"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -50 + 19x - 48x^2 = 5 $\n\nMove all terms to the left (standard form):\n$ -48x^2 + 19x + -55 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4267
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((-16 + -198/11) * 15) + 6^3 - log_9(729) + (-74 mod 11) + round(118/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-16 + -198/11) * 15) + 6^3 - log_9(729) + (-74 mod 11) + round(118/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 4268
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Compute the indefinite integral: $\\int (-2x + -9)e^{4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-2x + -9)e^{4x}\\,dx $\n\nUse standard antiderivatives (and integration by parts ... | {
"type": "calculus",
"seed": 1337,
"index": 4269
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. 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": 4270
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Evaluate: ((189 + 21/21) * 14) + 9^2 - log_7(16807) + (-309 mod 18) + floor(-161/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((189 + 21/21) * 14) + 9^2 - log_7(16807) + (-309 mod 18) + floor(-161/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 4271
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Solve for $x$ (in radians): tan(x) = \\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha ... | {
"type": "trigonometry",
"seed": 1337,
"index": 4272
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. 31 - 193x^2 - 114 = -31x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 31 - 193x^2 - 114 = -31x $\n\nMove all terms to the left (standard form):\n$ -193x^2 + 31x + -83 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4273
} |
[
{
"role": "user",
"content": "Can you solve the equation below? -2x - 144x^2 - 94 = -81"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -2x - 144x^2 - 94 = -81 $\n\nMove all terms to the left (standard form):\n$ -144x^2 + -2x + -13 = 0 $\n\nApply the quadratic formula:\n$ x = \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4274
} |
[
{
"role": "user",
"content": "solve: Prove that $f(x)=2x^2+-1x+-7$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=2x^2+-1x+-7$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 4x + -1 $\n$ f''(x) = 4 $\n\nSi... | {
"type": "optimization",
"seed": 1337,
"index": 4275
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. -48x^2 - 28 + 118 = -149x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -48x^2 - 28 + 118 = -149x $\n\nMove all terms to the left (standard form):\n$ -48x^2 + 149x + 90 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4276
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. -18x + 17 - 113 = 135x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -18x + 17 - 113 = 135x^2 $\n\nMove all terms to the left (standard form):\n$ -135x^2 + -18x + -96 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4277
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Evaluate: ((-169 + 150/25) * 20) + 4^5 - log_6(1296) + (423 mod 19) + round(110/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-169 + 150/25) * 20) + 4^5 - log_6(1296) + (423 mod 19) + round(110/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 4278
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. 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$ \\alph... | {
"type": "trigonometry",
"seed": 1337,
"index": 4279
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. 161 - 506x = -542"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 161 - 506x = -542 $\n\nMove all terms to the left (standard form):\n$ -506x + 703 = 0 $\n\nIsolate the $x$ term:\n$ -506x = -703 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 4280
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Compute $(-63+-191) \\bmod 10$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-63+-191) \\bmod 10 $\n\nUse the rule that addition is compatible with reduction mo... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4281
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Compute the determinant: $A=\\begin{pmatrix}-4&-4\\\\-3&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-4&-4\\\\\\-3&-4\\end{pmatrix} $\n\nUse... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4282
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. 27x - 38x^2 + 103 = 172"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 27x - 38x^2 + 103 = 172 $\n\nMove all terms to the left (standard form):\n$ -38x^2 + 27x + -69 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4283
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Evaluate: ((-89 + 637/13) * 1) + 7^2 - log_2(4) + (-21 mod 25) + ceil(122/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-89 + 637/13) * 1) + 7^2 - log_2(4) + (-21 mod 25) + ceil(122/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 4284
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Evaluate: ((80 + 100/10) * 5) + 12^5 - log_9(729) + (-155 mod 4) + floor(73/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((80 + 100/10) * 5) + 12^5 - log_9(729) + (-155 mod 4) + floor(73/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4285
} |
[
{
"role": "user",
"content": "solve 25x - 181 - 38 = -196x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 25x - 181 - 38 = -196x^2 $\n\nMove all terms to the left (standard form):\n$ 196x^2 + 25x + -219 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 -... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4286
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: 53x + 851 = 499"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 53x + 851 = 499 $\n\nMove all terms to the left (standard form):\n$ 53x + 352 = 0 $\n\nIsolate the $x$ term:\n$ 53x = -352 $\n\nDivide both sides by the coefficient of $x$:... | {
"type": "linear_equation",
"seed": 1337,
"index": 4287
} |
[
{
"role": "user",
"content": "solve: \n\n 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 solutions for $\\sin(x)=k$ ar... | {
"type": "trigonometry",
"seed": 1337,
"index": 4288
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Evaluate: ((-30 + 624/13) * 14) + 8^5 - log_10(1000) + (0 mod 24) + floor(-9/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-30 + 624/13) * 14) + 8^5 - log_10(1000) + (0 mod 24) + floor(-9/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 4289
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. -74 - 95x = -51"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -74 - 95x = -51 $\n\nMove all terms to the left (standard form):\n$ -95x + -23 = 0 $\n\nIsolate the $x$ term:\n$ -95x = 23 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 4290
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-5&-3\\\\\\-7&5\\end{pmatrix},\\quad b=\\begin{pmatrix}4\\\\\\70\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-5&-3\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4291
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Evaluate: ((-59 + 22/2) * 15) + 2^5 - log_8(262144) + (-27 mod 15) + ceil(178/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-59 + 22/2) * 15) + 2^5 - log_8(262144) + (-27 mod 15) + ceil(178/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 4292
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Prove that $f(x)=9x^2+1x+-2$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+1x+-2$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 18x ... | {
"type": "optimization",
"seed": 1337,
"index": 4293
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. -47x + 158 + 184 = 106x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -47x + 158 + 184 = 106x^2 $\n\nMove all terms to the left (standard form):\n$ -106x^2 + -47x + 342 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4294
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ ... | {
"type": "trigonometry",
"seed": 1337,
"index": 4295
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. 38x^2 - 152x - 6 = -175"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 38x^2 - 152x - 6 = -175 $\n\nMove all terms to the left (standard form):\n$ 38x^2 + -152x + 169 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4296
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 4297
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((32 + -800/20) * 2) + 3^5 - log_4(4096) + (435 mod 27) + round(-168/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((32 + -800/20) * 2) + 3^5 - log_4(4096) + (435 mod 27) + round(-168/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 4298
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Evaluate: ((70 + 950/25) * 10) + 3^5 - log_6(7776) + (-234 mod 6) + round(-158/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((70 + 950/25) * 10) + 3^5 - log_6(7776) + (-234 mod 6) + round(-... | {
"type": "arithmetic",
"seed": 1337,
"index": 4299
} |
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