messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Calculate the result of the given equation. Differentiate with respect to $x$: $f(x) = -5x^3 + 0x^2 + -15x + -6$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -5x^3 + 0x^2 + -15x + -6 $\n\nApply the standard differentiation rules:\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 1500
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Compute the determinant: $A=\\begin{pmatrix}-3&-7\\\\5&-5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-3&-7\\\\\\5&-5\\end{pmatrix} $\n\nUs... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1501
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Evaluate: ((159 + 80/20) * 9) + 4^2 - log_5(125) + (-18 mod 15) + round(142/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((159 + 80/20) * 9) + 4^2 - log_5(125) + (-18 mod 15) + round(142/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 1502
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. 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).... | {
"type": "trigonometry",
"seed": 1337,
"index": 1503
} |
[
{
"role": "user",
"content": "Provide the solution to the following 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).... | {
"type": "trigonometry",
"seed": 1337,
"index": 1504
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. 2 - 153x^2 + 76x = 79"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 2 - 153x^2 + 76x = 79 $\n\nMove all terms to the left (standard form):\n$ -153x^2 + 76x + -77 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1505
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. 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": 1506
} |
[
{
"role": "user",
"content": "Solve the equation shown below. 18 + 3x - 88x^2 = 91"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 18 + 3x - 88x^2 = 91 $\n\nMove all terms to the left (standard form):\n$ -88x^2 + 3x + -73 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1507
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. 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\\math... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1508
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. 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{Z... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1509
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Compute the indefinite integral: $\\int 4x^3 + -3x^2 + 4x + 14\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 4x^3 + -3x^2 + 4x + 14\\,dx $\n\nUse standard antiderivatives (and inte... | {
"type": "calculus",
"seed": 1337,
"index": 1510
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Compute the indefinite integral: $\\int \\ln(4x + -5)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(4x + -5)\\,dx $\n\nUse standard antiderivatives (and integration by parts... | {
"type": "calculus",
"seed": 1337,
"index": 1511
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Find $A^{-1}$ for $A=\\begin{pmatrix}9&-9\\\\3&-1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 9 & -9 \\\\ 3 & -1 \\end{pmatrix} $\n\nCompute the ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1512
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. -775 + 745x = 550"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -775 + 745x = 550 $\n\nMove all terms to the left (standard form):\n$ 745x + -1325 = 0 $\n\nIsolate the $x$ term:\n$ 745x = 1325 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 1513
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Prove that $f(x)=9x^2+2x+-3$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+2x+-3$.\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": 1514
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Evaluate: ((32 + 756/21) * 18) + 10^2 - log_5(3125) + (-409 mod 10) + floor(-135/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((32 + 756/21) * 18) + 10^2 - log_5(3125) + (-409 mod 10) + floor(-... | {
"type": "arithmetic",
"seed": 1337,
"index": 1515
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. 49 - 109 + 12x = 192x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 49 - 109 + 12x = 192x^2 $\n\nMove all terms to the left (standard form):\n$ -192x^2 + 12x + -60 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1516
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. -21x - 162x^2 - 158 = -11"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -21x - 162x^2 - 158 = -11 $\n\nMove all terms to the left (standard form):\n$ -162x^2 + -21x + -147 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1517
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. -683 + 367 = 923x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -683 + 367 = 923x $\n\nMove all terms to the left (standard form):\n$ -923x + -316 = 0 $\n\nIsolate the $x$ term:\n$ -923x = 316 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 1518
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Evaluate: ((-170 + -264/8) * 17) + 10^2 - log_6(216) + (210 mod 12) + ceil(-125/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-170 + -264/8) * 17) + 10^2 - log_6(216) + (210 mod 12) + ceil(-125/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 1519
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. 731 + 762 = -254x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 731 + 762 = -254x $\n\nMove all terms to the left (standard form):\n$ 254x + 1493 = 0 $\n\nIsolate the $x$ term:\n$ 254x = -1493 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 1520
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. 718 - 119x = 317"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 718 - 119x = 317 $\n\nMove all terms to the left (standard form):\n$ -119x + 401 = 0 $\n\nIsolate the $x$ term:\n$ -119x = -401 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 1521
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Evaluate: ((-149 + -720/15) * 3) + 3^2 - log_9(9) + (-326 mod 4) + ceil(-88/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-149 + -720/15) * 3) + 3^2 - log_9(9) + (-326 mod 4) + ceil(-88/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 1522
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n 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).\... | {
"type": "trigonometry",
"seed": 1337,
"index": 1523
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Evaluate: ((81 + -363/11) * 5) + 9^3 - log_3(81) + (-29 mod 11) + round(-3/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((81 + -363/11) * 5) + 9^3 - log_3(81) + (-29 mod 11) + round(-3/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 1524
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. -500 + 912x = 825"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -500 + 912x = 825 $\n\nMove all terms to the left (standard form):\n$ 912x + -1325 = 0 $\n\nIsolate the $x$ term:\n$ 912x = 1325 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 1525
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Prove that $(\\mathbb{Z}_21, +)$ is a group under addition modulo 21."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_21=\\{0,1,\\dots,20\\}$ with operation $+$ modulo $21$.\n\n**Closure:** If $a,b\\in\\mathbb{Z... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1526
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. 172 - 848x = -300"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 172 - 848x = -300 $\n\nMove all terms to the left (standard form):\n$ -848x + 472 = 0 $\n\nIsolate the $x$ term:\n$ -848x = -472 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 1527
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 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 genera... | {
"type": "trigonometry",
"seed": 1337,
"index": 1528
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Find the modular inverse of 6 modulo 13, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $6\\cdot a^{-1} \\equiv 1 \\pmod{13}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1529
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Evaluate: ((87 + 161/7) * 20) + 7^4 - log_3(9) + (222 mod 29) + round(-153/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((87 + 161/7) * 20) + 7^4 - log_3(9) + (222 mod 29) + round(-153/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 1530
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. 398x + 792 = -34"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 398x + 792 = -34 $\n\nMove all terms to the left (standard form):\n$ 398x + 826 = 0 $\n\nIsolate the $x$ term:\n$ 398x = -826 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 1531
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}1&-3&4\\\\\\5&-3&2\\\\\\-4&5&2\\end{pmatrix},\\quad b=\\begin{pmatrix}0\\\\\\18\\\\\\-33\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1532
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}4&9\\\\5&-1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 4 & 9 \\\\ 5 & -1 \\end{pmatrix} $\n\nCompute t... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1533
} |
[
{
"role": "user",
"content": "Please find and report 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)... | {
"type": "optimization",
"seed": 1337,
"index": 1534
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. 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": 1535
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((-192 + -460/10) * 19) + 2^3 - log_2(2) + (500 mod 9) + round(-29/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-192 + -460/10) * 19) + 2^3 - log_2(2) + (500 mod 9) + round(-29/2) $\n\nCompute each ... | {
"type": "arithmetic",
"seed": 1337,
"index": 1536
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. 213 + 173 = 916x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 213 + 173 = 916x $\n\nMove all terms to the left (standard form):\n$ -916x + 386 = 0 $\n\nIsolate the $x$ term:\n$ -916x = -386 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 1537
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Compute the indefinite integral: $\\int \\ln(8x + 4)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(8x + 4)\\,dx $\n\nUse standard antiderivatives (and integration by parts i... | {
"type": "calculus",
"seed": 1337,
"index": 1538
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. -4 + 155x + 152x^2 = 110"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -4 + 155x + 152x^2 = 110 $\n\nMove all terms to the left (standard form):\n$ 152x^2 + 155x + -114 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1539
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Compute the indefinite integral: $\\int 1e^{-1x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 1e^{-1x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\... | {
"type": "calculus",
"seed": 1337,
"index": 1540
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. 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(\\f... | {
"type": "trigonometry",
"seed": 1337,
"index": 1541
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Evaluate: ((144 + -440/11) * 7) + 3^4 - log_6(7776) + (368 mod 4) + floor(-8/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((144 + -440/11) * 7) + 3^4 - log_6(7776) + (368 mod 4) + floor(-... | {
"type": "arithmetic",
"seed": 1337,
"index": 1542
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Prove that $f(x)=6x^2+-3x+-4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=6x^2+-3x+-4$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$... | {
"type": "optimization",
"seed": 1337,
"index": 1543
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((94 + -54/6) * 13) + 8^3 - log_4(64) + (-406 mod 29) + round(192/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((94 + -54/6) * 13) + 8^3 - log_4(64) + (-406 mod 29) + round(192/2) $\n\nCompute each co... | {
"type": "arithmetic",
"seed": 1337,
"index": 1544
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}3&6\\\\\\-3&-8\\end{pmatrix},\\quad b=\\begin{pmatrix}-6\\\\\\0\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}3&6\\\\\\-3&-8\\end{pma... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1545
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Prove that $f(x)=10x^2+9x+-4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=10x^2+9x+-4$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ ... | {
"type": "optimization",
"seed": 1337,
"index": 1546
} |
[
{
"role": "user",
"content": "Work out the result of this equation. 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 = \\arctan(-\\... | {
"type": "trigonometry",
"seed": 1337,
"index": 1547
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 269 - 257 = -609x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 269 - 257 = -609x $\n\nMove all terms to the left (standard form):\n$ 609x + 12 = 0 $\n\nIsolate the $x$ term:\n$ 609x = -12 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 1548
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Prove that $f(x)=7x^2+0x+-6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=7x^2+0x+-6$.\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": 1549
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Evaluate: ((178 + 99/11) * 11) + 12^5 - log_3(729) + (-299 mod 14) + ceil(162/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((178 + 99/11) * 11) + 12^5 - log_3(729) + (-299 mod 14) + ceil(162/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 1550
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Differentiate with respect to $x$: $f(x) = -3x^3 + -4x^2 + 19x + 12$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3x^3 + -4x^2 + 19x + 12 $\n\nApply the standard differentiation rules:\n$ f'... | {
"type": "calculus",
"seed": 1337,
"index": 1551
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Differentiate with respect to $x$: $f(x) = (-2x + 0)e^{3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-2x + 0)e^{3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed... | {
"type": "calculus",
"seed": 1337,
"index": 1552
} |
[
{
"role": "user",
"content": "Please compute the answer to this 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{\\p... | {
"type": "optimization",
"seed": 1337,
"index": 1553
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Evaluate: ((176 + 48/12) * 14) + 5^5 - log_10(1000) + (396 mod 11) + floor(40/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((176 + 48/12) * 14) + 5^5 - log_10(1000) + (396 mod 11) + floor(40/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 1554
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Differentiate with respect to $x$: $f(x) = -1e^{2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1e^{2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-2e^{2x}} $"
... | {
"type": "calculus",
"seed": 1337,
"index": 1555
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Prove that $(\\mathbb{Z}_5, +)$ is a group under addition modulo 5."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_5=\\{0,1,\\dots,4\\}$ with operation $+$ modulo $5$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, then $(a+b... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1556
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. -3 - 122x^2 + 179x = -48"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -3 - 122x^2 + 179x = -48 $\n\nMove all terms to the left (standard form):\n$ -122x^2 + 179x + 45 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1557
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Evaluate: ((118 + -120/12) * 8) + 2^5 - log_6(6) + (125 mod 10) + floor(175/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((118 + -120/12) * 8) + 2^5 - log_6(6) + (125 mod 10) + floor(175/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 1558
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Compute the indefinite integral: $\\int -4\\sin(9x) + -2\\cos(9x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -4\\sin(9x) + -2\\cos(9x)\\,dx $\n\nUse standard antiderivatives (and i... | {
"type": "calculus",
"seed": 1337,
"index": 1559
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-1&8\\\\\\7&6\\end{pmatrix},\\quad b=\\begin{pmatrix}18\\\\\\60\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-1&8\\\\\\7&6\\end{p... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1560
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Evaluate: ((-160 + -80/5) * 19) + 3^2 - log_7(117649) + (-190 mod 24) + round(-82/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-160 + -80/5) * 19) + 3^2 - log_7(117649) + (-190 mod 24) + round(-82/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 1561
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Prove that $(\\mathbb{Z}_26, +)$ is a group under addition modulo 26."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_26=\\{0,1,\\dots,25\\}$ with operation $+$ modulo $26$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, then... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1562
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. 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$ \\alp... | {
"type": "trigonometry",
"seed": 1337,
"index": 1563
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Differentiate with respect to $x$: $f(x) = -5x^3 + -9x^2 + -19x + -17$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -5x^3 + -9x^2 + -19x + -17 $\n\nApply the standard differentiation ru... | {
"type": "calculus",
"seed": 1337,
"index": 1564
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Prove that $f(x,y)=\\frac12(4x^2+7y^2)+-2x+5y+-9$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(4x^2+7y^2)+-2x+5y+-9 $\n\n$ \\frac{\\partial^2 f}{... | {
"type": "optimization",
"seed": 1337,
"index": 1565
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-8&-6\\\\-6&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -8 & -6 \\\\ -6 & 1 \\end{pmatrix} $\n\nComput... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1566
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. 33x - 861 = 503"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 33x - 861 = 503 $\n\nMove all terms to the left (standard form):\n$ 33x + -1364 = 0 $\n\nIsolate the $x$ term:\n$ 33x = 1364 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 1567
} |
[
{
"role": "user",
"content": "Can you find the solution to 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$ ... | {
"type": "trigonometry",
"seed": 1337,
"index": 1568
} |
[
{
"role": "user",
"content": "Find the numerical solution to this 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": 1569
} |
[
{
"role": "user",
"content": "Please calculate this 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 = \\arccos(-\\frac{1... | {
"type": "trigonometry",
"seed": 1337,
"index": 1570
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. 653x - 893 = -658"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 653x - 893 = -658 $\n\nMove all terms to the left (standard form):\n$ 653x + -235 = 0 $\n\nIsolate the $x$ term:\n$ 653x = 235 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 1571
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. 17x + 166x^2 + 122 = 153"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 17x + 166x^2 + 122 = 153 $\n\nMove all terms to the left (standard form):\n$ 166x^2 + 17x + -31 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1572
} |
[
{
"role": "user",
"content": "solve: 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(-\\frac{1}{2}) = 2.0944 $\n\nThe ... | {
"type": "trigonometry",
"seed": 1337,
"index": 1573
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Evaluate: ((158 + 552/24) * 15) + 8^4 - log_2(32) + (-201 mod 27) + round(128/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((158 + 552/24) * 15) + 8^4 - log_2(32) + (-201 mod 27) + round(128/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 1574
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-7&5\\\\\\7&6\\end{pmatrix},\\quad b=\\begin{pmatrix}-14\\\\\\91\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-7&5\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1575
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Evaluate: ((89 + 20/10) * 17) + 3^4 - log_8(262144) + (-258 mod 12) + floor(-101/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((89 + 20/10) * 17) + 3^4 - log_8(262144) + (-258 mod 12) + floor(-... | {
"type": "arithmetic",
"seed": 1337,
"index": 1576
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. -50x^2 + 124 + 33 = -181x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -50x^2 + 124 + 33 = -181x $\n\nMove all terms to the left (standard form):\n$ -50x^2 + 181x + 157 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1577
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Evaluate: ((-69 + 240/16) * 15) + 10^5 - log_2(32) + (258 mod 17) + round(-41/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-69 + 240/16) * 15) + 10^5 - log_2(32) + (258 mod 17) + round(-41/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 1578
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Find $A^{-1}$ for $A=\\begin{pmatrix}3&8\\\\1&-6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 3 & 8 \\\\ 1 & -6 \\end{pmatrix} $\n\nCompute... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1579
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Compute the indefinite integral: $\\int -1x^3 + 8x^2 + -18x + -16\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -1x^3 + 8x^2 + -18x + -16\\,dx $\n\nUse standard antiderivatives (... | {
"type": "calculus",
"seed": 1337,
"index": 1580
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Find $A^{-1}$ for $A=\\begin{pmatrix}8&8\\\\2&0\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 8 & 8 \\\\ 2 & 0 \\end{pmatrix} $\n\nCompute the determinant: $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1581
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((-122 + -861/21) * 19) + 7^4 - log_10(100) + (-365 mod 6) + ceil(-198/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-122 + -861/21) * 19) + 7^4 - log_10(100) + (-365 mod 6) + ceil(-198/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 1582
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Compute the determinant: $A=\\begin{pmatrix}3&8\\\\-1&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}3&8\\\\\\-1&-4\\end{pmatrix} $\n\nU... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1583
} |
[
{
"role": "user",
"content": "Can you solve the equation below? 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 integer... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1584
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Evaluate: ((75 + 247/13) * 7) + 7^3 - log_3(243) + (-473 mod 4) + floor(-66/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((75 + 247/13) * 7) + 7^3 - log_3(243) + (-473 mod 4) + floor(-66/2) $\n\nCompute each component:\n$ 247... | {
"type": "arithmetic",
"seed": 1337,
"index": 1585
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Evaluate: ((-120 + -612/17) * 4) + 4^4 - log_3(243) + (-446 mod 5) + ceil(2/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-120 + -612/17) * 4) + 4^4 - log_3(243) + (-446 mod 5) + ceil(2/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 1586
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. 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": 1587
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Prove that $f(x)=7x^2+-3x+4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=7x^2+-3x+4$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 14... | {
"type": "optimization",
"seed": 1337,
"index": 1588
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Evaluate: ((26 + -392/8) * 15) + 3^4 - log_4(16) + (-434 mod 10) + round(-18/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((26 + -392/8) * 15) + 3^4 - log_4(16) + (-434 mod 10) + round(-18/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 1589
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 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^... | {
"type": "optimization",
"seed": 1337,
"index": 1590
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&0&0\\\\\\3&-1&-3\\\\\\0&-5&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}20\\\\\\-8\\\\\\8\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1591
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. -947x - 765 = 353"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -947x - 765 = 353 $\n\nMove all terms to the left (standard form):\n$ -947x + -1118 = 0 $\n\nIsolate the $x$ term:\n$ -947x = 1118 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 1592
} |
[
{
"role": "user",
"content": "Can you compute this equation? 665 + 114x = -683"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 665 + 114x = -683 $\n\nMove all terms to the left (standard form):\n$ 114x + 1348 = 0 $\n\nIsolate the $x$ term:\n$ 114x = -1348 $\n\nDivide both sides by ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1593
} |
[
{
"role": "user",
"content": "Find the solution to this math 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:\n$... | {
"type": "optimization",
"seed": 1337,
"index": 1594
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Evaluate: ((182 + -468/18) * 20) + 7^3 - log_4(4) + (-234 mod 14) + ceil(135/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((182 + -468/18) * 20) + 7^3 - log_4(4) + (-234 mod 14) + ceil(135/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 1595
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Prove that $f(x)=9x^2+9x+-10$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+9x+-10$.\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": 1596
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Evaluate: ((-73 + 16/16) * 17) + 10^4 - log_10(1000000) + (235 mod 10) + floor(114/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-73 + 16/16) * 17) + 10^4 - log_10(1000000) + (235 mod 10) + floor(11... | {
"type": "arithmetic",
"seed": 1337,
"index": 1597
} |
[
{
"role": "user",
"content": "Find the value that satisfies 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 gene... | {
"type": "trigonometry",
"seed": 1337,
"index": 1598
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Differentiate with respect to $x$: $f(x) = \\ln(8x + -2)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(8x + -2) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{8}{8x ... | {
"type": "calculus",
"seed": 1337,
"index": 1599
} |
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