messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Please evaluate and solve this equation. 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 value).\n$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 1100
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-6&-1\\\\\\-3&8\\end{pmatrix},\\quad b=\\begin{pmatrix}5\\\\\\-40\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-6&-1\\\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1101
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&3&-5\\\\\\4&-4&-3\\\\\\1&5&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}-16\\\\\\-5\\\\\\-26\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1102
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Solve for $x$ (in radians): sin(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin... | {
"type": "trigonometry",
"seed": 1337,
"index": 1103
} |
[
{
"role": "user",
"content": "Please solve this math problem. Find $A^{-1}$ for $A=\\begin{pmatrix}-9&-9\\\\4&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -9 & -9 \\\\ 4 & -4 \\end{pmatrix} $\n\nCompute the determina... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1104
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. -49x^2 + 175 + 33 = 19x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -49x^2 + 175 + 33 = 19x $\n\nMove all terms to the left (standard form):\n$ -49x^2 + -19x + 208 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1105
} |
[
{
"role": "user",
"content": "Please solve this math problem. 46 - 57 - 42x = -13x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 46 - 57 - 42x = -13x^2 $\n\nMove all terms to the left (standard form):\n$ 13x^2 + -42x + -11 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1106
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. 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": 1107
} |
[
{
"role": "user",
"content": "Determine the value produced by 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).\... | {
"type": "trigonometry",
"seed": 1337,
"index": 1108
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Compute the indefinite integral: $\\int -3x^3 + -3x^2 + -16x + -17\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -3x^3 + -3x^2 + -16x + -17\\,dx $\n\nUse standard antiderivatives (... | {
"type": "calculus",
"seed": 1337,
"index": 1109
} |
[
{
"role": "user",
"content": "Please calculate this equation. Compute the determinant: $A=\\begin{pmatrix}-7&7\\\\5&-6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-7&7\\\\\\5&-6\\end{pmatrix} $\n\nUse $\\det(A)=a... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1110
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Evaluate: ((119 + 369/9) * 13) + 5^4 - log_10(10000) + (-206 mod 9) + round(192/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((119 + 369/9) * 13) + 5^4 - log_10(10000) + (-206 mod 9) + round(192/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 1111
} |
[
{
"role": "user",
"content": "Solve the following math equation. Evaluate: ((-91 + 819/21) * 5) + 11^4 - log_3(729) + (-495 mod 16) + round(48/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-91 + 819/21) * 5) + 11^4 - log_3(729) + (-495 mod 16) + round(48/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 1112
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}0&1&0\\\\\\3&3&-3\\\\\\1&-1&4\\end{pmatrix},\\quad b=\\begin{pmatrix}0\\\\\\3\\\\\\-9\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g.,... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1113
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Solve for $x$ (in radians): tan(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 0 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(0) = 0 $\n\nThe genera... | {
"type": "trigonometry",
"seed": 1337,
"index": 1114
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. -593x + 259 = -706"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -593x + 259 = -706 $\n\nMove all terms to the left (standard form):\n$ -593x + 965 = 0 $\n\nIsolate the $x$ term:\n$ -593x = -965 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 1115
} |
[
{
"role": "user",
"content": "Please work out this equation. Prove that $f(x)=5x^2+-3x+8$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+-3x+8$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 10x + -3 $... | {
"type": "optimization",
"seed": 1337,
"index": 1116
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Evaluate: ((-36 + 60/6) * 6) + 10^4 - log_9(9) + (-114 mod 6) + ceil(-166/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-36 + 60/6) * 6) + 10^4 - log_9(9) + (-114 mod 6) + ceil(-166/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 1117
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}9&-9\\\\8&-2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 9 & -9 \\\\ 8 & -2 \\end{pmatrix} $\n\nCompute th... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1118
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Compute the determinant: $A=\\begin{pmatrix}8&-5\\\\7&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}8&-5\\\\\\7&1\\end{pmatrix} $\n\nUse $\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1119
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Compute the determinant: $A=\\begin{pmatrix}-7&-7\\\\8&-6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-7&-7\\\\\\8&-6\\end{pmatrix} $\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1120
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Evaluate: ((164 + 966/21) * 9) + 11^5 - log_8(4096) + (-188 mod 3) + floor(0/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((164 + 966/21) * 9) + 11^5 - log_8(4096) + (-188 mod 3) + floor(0/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 1121
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Compute the indefinite integral: $\\int (3x + -8)\\sin(6x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (3x + -8)\\sin(6x)\\,dx $\n\nUse standard antiderivatives (and integration by ... | {
"type": "calculus",
"seed": 1337,
"index": 1122
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. -198x - 256 = -157"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -198x - 256 = -157 $\n\nMove all terms to the left (standard form):\n$ -198x + -99 = 0 $\n\nIsolate the $x$ term:\n$ -198x = 99 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 1123
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&0&-5\\\\\\-4&3&-2\\\\\\2&3&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}-25\\\\\\8\\\\\\-7\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1124
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Evaluate: ((-162 + 154/7) * 17) + 5^3 - log_2(32) + (117 mod 12) + ceil(-191/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-162 + 154/7) * 17) + 5^3 - log_2(32) + (117 mod 12) + ceil(-191/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 1125
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Evaluate: ((-158 + -165/15) * 4) + 8^4 - log_4(16) + (-477 mod 11) + ceil(9/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-158 + -165/15) * 4) + 8^4 - log_4(16) + (-477 mod 11) + ceil(9/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 1126
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Evaluate: ((54 + 0/14) * 20) + 6^2 - log_10(100) + (-259 mod 12) + round(152/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((54 + 0/14) * 20) + 6^2 - log_10(100) + (-259 mod 12) + round(152... | {
"type": "arithmetic",
"seed": 1337,
"index": 1127
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Solve for $x$ (in radians): cos(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = 0 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(0) = 1.5708 $\n\n... | {
"type": "trigonometry",
"seed": 1337,
"index": 1128
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. 30x^2 - 70 + 9x = 69"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 30x^2 - 70 + 9x = 69 $\n\nMove all terms to the left (standard form):\n$ 30x^2 + 9x + -139 = 0 $\n\nApply the quadratic formula:\n$ x = \\fr... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1129
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Compute $(162+-96) \\bmod 17$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (162+-96) \\bmod 17 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1130
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. 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": 1131
} |
[
{
"role": "user",
"content": "Can you compute this equation? Find the modular inverse of 9 modulo 38, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $9\\cdot a^{-1} \\equiv 1 \\pmod{38}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integers $... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1132
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. x + 112 + 59 = 45x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ x + 112 + 59 = 45x^2 $\n\nMove all terms to the left (standard form):\n$ -45x^2 + 1x + 171 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1133
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. -44 + 168x^2 - 150 = -33x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -44 + 168x^2 - 150 = -33x $\n\nMove all terms to the left (standard form):\n$ 168x^2 + 33x + -194 = 0 $\n\nApply the quadratic ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1134
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Evaluate: ((85 + -297/11) * 3) + 2^2 - log_7(2401) + (-434 mod 26) + ceil(198/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((85 + -297/11) * 3) + 2^2 - log_7(2401) + (-434 mod 26) + ceil(1... | {
"type": "arithmetic",
"seed": 1337,
"index": 1135
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Compute the indefinite integral: $\\int -3\\sin(8x) + -4\\cos(5x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -3\\sin(8x) + -4\\cos(5x)\\,dx $\n\nUse standard antiderivatives (and i... | {
"type": "calculus",
"seed": 1337,
"index": 1136
} |
[
{
"role": "user",
"content": "Please work out this equation. -20 - 129x^2 - 34 = -107x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -20 - 129x^2 - 34 = -107x $\n\nMove all terms to the left (standard form):\n$ -129x^2 + 107x + -54 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1137
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Prove that $(\\mathbb{Z}_25, +)$ is a group under addition modulo 25."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_25=\\{0,1,\\dots,24\\}$ with operation $+$ modulo $25$.\n\n**Closure:** If $a,b\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1138
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}5&-1\\\\\\1&-9\\end{pmatrix},\\quad b=\\begin{pmatrix}-8\\\\\\-28\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}5&-1\\\\\\1&-9\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1139
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Compute $(179+133) \\bmod 19$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (179+133) \\bmod 19 $\n\nUse the rule that addition is compatible with reduction modul... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1140
} |
[
{
"role": "user",
"content": "Solve the following math equation. Evaluate: ((165 + 1032/24) * 1) + 2^3 - log_8(262144) + (75 mod 27) + round(141/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((165 + 1032/24) * 1) + 2^3 - log_8(262144) + (75 mod 27) + round(141/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 1141
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. 50 - 61 + 179x = 160x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 50 - 61 + 179x = 160x^2 $\n\nMove all terms to the left (standard form):\n$ -160x^2 + 179x + -11 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1142
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Evaluate: ((-120 + 220/10) * 6) + 11^3 - log_10(1000) + (-276 mod 27) + round(-149/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-120 + 220/10) * 6) + 11^3 - log_10(1000) + (-276 mod 27) + round... | {
"type": "arithmetic",
"seed": 1337,
"index": 1143
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Evaluate: ((-170 + -616/14) * 3) + 11^3 - log_10(10000) + (188 mod 23) + ceil(-197/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-170 + -616/14) * 3) + 11^3 - log_10(10000) + (188 mod 23) + ceil(... | {
"type": "arithmetic",
"seed": 1337,
"index": 1144
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Evaluate: ((-144 + 924/21) * 4) + 6^5 - log_5(125) + (74 mod 4) + ceil(161/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-144 + 924/21) * 4) + 6^5 - log_5(125) + (74 mod 4) + ceil(161/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 1145
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Evaluate: ((133 + 782/23) * 18) + 8^5 - log_2(8) + (316 mod 16) + round(198/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((133 + 782/23) * 18) + 8^5 - log_2(8) + (316 mod 16) + round(198/2) $\n\nCompute each ... | {
"type": "arithmetic",
"seed": 1337,
"index": 1146
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Prove that $(\\mathbb{Z}_27, +)$ is a group under addition modulo 27."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_27=\\{0,1,\\dots,26\\}$ with operation $+$ modulo $27$.\n\n**Closure:** If $a,b\\in\\math... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1147
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}8&3\\\\\\5&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}3\\\\\\-4\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}8&3\\\\\\5&-4\\end{pmatr... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1148
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. -24 - 18 - 194x^2 = -168x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -24 - 18 - 194x^2 = -168x $\n\nMove all terms to the left (standard form):\n$ -194x^2 + 168x + -42 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1149
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Evaluate: ((40 + 64/4) * 11) + 7^3 - log_3(27) + (385 mod 20) + floor(88/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((40 + 64/4) * 11) + 7^3 - log_3(27) + (385 mod 20) + floor(88/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 1150
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Evaluate: ((61 + -90/3) * 11) + 4^5 - log_8(4096) + (-300 mod 4) + round(112/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((61 + -90/3) * 11) + 4^5 - log_8(4096) + (-300 mod 4) + round(1... | {
"type": "arithmetic",
"seed": 1337,
"index": 1151
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Compute the indefinite integral: $\\int 2e^{5x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 2e^{5x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if... | {
"type": "calculus",
"seed": 1337,
"index": 1152
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Compute the indefinite integral: $\\int (-2x + -1)e^{5x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-2x + -1)e^{5x}\\,dx $\n\nUse standard antiderivatives (and integr... | {
"type": "calculus",
"seed": 1337,
"index": 1153
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Find the modular inverse of 4 modulo 15, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $4\\cdot a^{-1} \\equiv 1 \\pmod{15}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1154
} |
[
{
"role": "user",
"content": "Please work out this equation. -877 - 426x = -612"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -877 - 426x = -612 $\n\nMove all terms to the left (standard form):\n$ -426x + -265 = 0 $\n\nIsolate the $x$ term:\n$ -426x = 265 $\n\nDivide both sides b... | {
"type": "linear_equation",
"seed": 1337,
"index": 1155
} |
[
{
"role": "user",
"content": "solve Solve for $x$ (in radians): tan(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 1 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(1) = 0.785398 $\n\nThe general solutions for $\\tan(x)=k$ ... | {
"type": "trigonometry",
"seed": 1337,
"index": 1156
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Compute the indefinite integral: $\\int 9\\sin(4x) + -5\\cos(1x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 9\\sin(4x) + -5\\cos(1x)\\,dx $\n\nUse standard antiderivatives ... | {
"type": "calculus",
"seed": 1337,
"index": 1157
} |
[
{
"role": "user",
"content": "Solve the following math equation. -42 - 180x - 158 = -38x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -42 - 180x - 158 = -38x^2 $\n\nMove all terms to the left (standard form):\n$ 38x^2 + -180x + -200 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1158
} |
[
{
"role": "user",
"content": "Work through and solve this equation. 56 + 224 = 850x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 56 + 224 = 850x $\n\nMove all terms to the left (standard form):\n$ -850x + 280 = 0 $\n\nIsolate the $x$ term:\n$ -850x = -280 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1159
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Prove that $(\\mathbb{Z}_24, +)$ is a group under addition modulo 24."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_24=\\{0,1,\\dots,23\\}$ with operation $+$ modulo $24$.\n\n**Closure:** If $a,b\\in\\mathbb{... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1160
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Prove that $f(x,y)=\\frac12(10x^2+6y^2)+-1x+4y+4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(10x^2+6y^2)+-1x+4y+4 $\n\n$ \\frac{\\partial^2... | {
"type": "optimization",
"seed": 1337,
"index": 1161
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Evaluate: ((38 + -220/10) * 7) + 11^2 - log_5(3125) + (442 mod 8) + ceil(-23/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((38 + -220/10) * 7) + 11^2 - log_5(3125) + (442 mod 8) + ceil(-23/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 1162
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. 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": 1163
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. 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": 1164
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. 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) = -1.5... | {
"type": "trigonometry",
"seed": 1337,
"index": 1165
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Evaluate: ((-99 + 779/19) * 12) + 10^4 - log_5(5) + (-159 mod 9) + floor(82/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-99 + 779/19) * 12) + 10^4 - log_5(5) + (-159 mod 9) + floor(82/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 1166
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. 326 - 552 = -156x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 326 - 552 = -156x $\n\nMove all terms to the left (standard form):\n$ 156x + -226 = 0 $\n\nIsolate the $x$ term:\n$ 156x = 226 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1167
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&3&-4\\\\\\3&-4&-5\\\\\\-4&-4&1\\end{pmatrix},\\quad b=\\begin{pmatrix}9\\\\\\-12\\\\\\-12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1168
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. 711 - 818x = -162"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 711 - 818x = -162 $\n\nMove all terms to the left (standard form):\n$ -818x + 873 = 0 $\n\nIsolate the $x$ term:\n$ -818x = -873 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 1169
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Compute the determinant: $A=\\begin{pmatrix}9&-6\\\\-4&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}9&-6\\\\\\-4&2\\end{pmatrix} $\n\nUse $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1170
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. 49x^2 + 115 + 136 = -104x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 49x^2 + 115 + 136 = -104x $\n\nMove all terms to the left (standard form):\n$ 49x^2 + 104x + 251 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1171
} |
[
{
"role": "user",
"content": "Please determine the solution to 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).... | {
"type": "trigonometry",
"seed": 1337,
"index": 1172
} |
[
{
"role": "user",
"content": "Please determine the outcome of this 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 $\n\nThe ge... | {
"type": "trigonometry",
"seed": 1337,
"index": 1173
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. -342 - 107x = -181"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -342 - 107x = -181 $\n\nMove all terms to the left (standard form):\n$ -107x + -161 = 0 $\n\nIsolate the $x$ term:\n$ -107x = 161 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 1174
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. -45 - 681 = 472x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -45 - 681 = 472x $\n\nMove all terms to the left (standard form):\n$ -472x + -726 = 0 $\n\nIsolate the $x$ term:\n$ -472x = 726 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1175
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. 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 value).\n$ ... | {
"type": "trigonometry",
"seed": 1337,
"index": 1176
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Compute the determinant: $A=\\begin{pmatrix}-3&-7\\\\5&-3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-3&-7\\\\\\5&-3\\end{pmatrix}... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1177
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Compute the determinant: $A=\\begin{pmatrix}-7&8\\\\3&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-7&8\\\\\\3&2\\end{pmatrix} $\n\nUse $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1178
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Prove that $(\\mathbb{Z}_17, +)$ is a group under addition modulo 17."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_17=\\{0,1,\\dots,16\\}$ with operation $+$ modulo $17$.\n\n**Closure:** If $a,b\\in\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1179
} |
[
{
"role": "user",
"content": "solve: Prove that $f(x,y)=\\frac12(5x^2+2y^2)+1x+5y+-6$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(5x^2+2y^2)+1x+5y+-6 $\n\n$ \\frac{\\partial^2 f}{\\partial x^2} = 5,\\quad \\frac{\\par... | {
"type": "optimization",
"seed": 1337,
"index": 1180
} |
[
{
"role": "user",
"content": "Solve the equation shown below. -993 - 818 = -880x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -993 - 818 = -880x $\n\nMove all terms to the left (standard form):\n$ 880x + -1811 = 0 $\n\nIsolate the $x$ term:\n$ 880x = 1811 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1181
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Find $A^{-1}$ for $A=\\begin{pmatrix}4&-4\\\\-4&3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 4 & -4 \\\\ -4 & 3 \\end{pmatrix} $\n\nCompute the ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1182
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Prove that $(\\mathbb{Z}_27, +)$ is a group under addition modulo 27."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_27=\\{0,1,\\dots,26\\}$ with operation $+$ modulo $27$.\n\n**Closure:** If $a,b\\in\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1183
} |
[
{
"role": "user",
"content": "Please solve this math problem. Compute the indefinite integral: $\\int (-5x + -6)e^{4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-5x + -6)e^{4x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if need... | {
"type": "calculus",
"seed": 1337,
"index": 1184
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n 684x + 345 = 121"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 684x + 345 = 121 $\n\nMove all terms to the left (standard form):\n$ 684x + 224 = 0 $\n\nIsolate the $x$ term:\n$ 684x = -224 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 1185
} |
[
{
"role": "user",
"content": "Compute the solution 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 $f'(x)=0$, hence:\n$ ... | {
"type": "optimization",
"seed": 1337,
"index": 1186
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? -415x + 437 = -219"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -415x + 437 = -219 $\n\nMove all terms to the left (standard form):\n$ -415x + 656 = 0 $\n\nIsolate the $x$ term:\n$ -415x = -656 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 1187
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Solve for $x$ (in radians): sin(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 1188
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. 398x - 233 = 862"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 398x - 233 = 862 $\n\nMove all terms to the left (standard form):\n$ 398x + -1095 = 0 $\n\nIsolate the $x$ term:\n$ 398x = 1095 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 1189
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. -47 + 4x - 88x^2 = 39"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -47 + 4x - 88x^2 = 39 $\n\nMove all terms to the left (standard form):\n$ -88x^2 + 4x + -86 = 0 $\n\nApply the quadratic formula:\n$ x = \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1190
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Prove that $(\\mathbb{Z}_11, +)$ is a group under addition modulo 11."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_11=\\{0,1,\\dots,10\\}$ with operation $+$ modulo $11$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, th... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1191
} |
[
{
"role": "user",
"content": "Solve this equation accurately. 900 + 77 = 210x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 900 + 77 = 210x $\n\nMove all terms to the left (standard form):\n$ -210x + 977 = 0 $\n\nIsolate the $x$ term:\n$ -210x = -977 $\n\nDivide both sides by the... | {
"type": "linear_equation",
"seed": 1337,
"index": 1192
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. -x^2 - 94 + 58x = -160"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -x^2 - 94 + 58x = -160 $\n\nMove all terms to the left (standard form):\n$ -1x^2 + 58x + 66 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1193
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. 249 - 255 = 585x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 249 - 255 = 585x $\n\nMove all terms to the left (standard form):\n$ -585x + -6 = 0 $\n\nIsolate the $x$ term:\n$ -585x = 6 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 1194
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Differentiate with respect to $x$: $f(x) = (5x + -6)\\sin(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (5x + -6)\\sin(5x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{5\... | {
"type": "calculus",
"seed": 1337,
"index": 1195
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Evaluate: ((137 + -819/21) * 15) + 11^5 - log_10(1000000) + (-397 mod 2) + floor(55/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((137 + -819/21) * 15) + 11^5 - log_10(1000000) + (-397 mod 2) + flo... | {
"type": "arithmetic",
"seed": 1337,
"index": 1196
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. -559x + 222 = -124"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -559x + 222 = -124 $\n\nMove all terms to the left (standard form):\n$ -559x + 346 = 0 $\n\nIsolate the $x$ term:\n$ -559x = -346 $\n\nDi... | {
"type": "linear_equation",
"seed": 1337,
"index": 1197
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Prove that $(\\mathbb{Z}_28, +)$ is a group under addition modulo 28."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_28=\\{0,1,\\dots,27\\}$ with operation $+$ modulo $28$.\n\n**Closure:** If $a,b\\in\\mathbb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1198
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Compute the indefinite integral: $\\int 9\\sin(2x) + -4\\cos(5x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 9\\sin(2x) + -4\\cos(5x)\\,dx $\n\nUse standard antiderivatives (and... | {
"type": "calculus",
"seed": 1337,
"index": 1199
} |
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