{
"cells": [
{
"id": 0,
"input": "diff sin(x^2)",
"output": "simplified = 2*x*cos(x^2)"
},
{
"id": 1,
"input": "diff x^3 + 2*x^2 - 5*x + 1",
"output": "simplified = 3*x^2 + 4*x - 5"
},
{
"id": 2,
"input": "integrate x^2",
"output": "= x^3/3 + C"
},
{
"id": 3,
"input": "integrate sin(x)",
"output": "= -cos(x) + C"
},
{
"id": 4,
"input": "integrate exp(x)",
"output": "= exp(x) + C"
},
{
"id": 5,
"input": "int sin(x) 0 pi",
"output": "2"
},
{
"id": 6,
"input": "romberg exp(x) 0 1 10",
"output": "1.7182818284590455"
},
{
"id": 7,
"input": "taylor sin(x) 0 7",
"output": "f(x) \u2248 x - 0.16666666666666666*x^3 + 0.008333333333333333*x^5 - 0.0001984126984126984*x^7"
},
{
"id": 8,
"input": "taylor cos(x) 0 6",
"output": "f(x) \u2248 1 - 0.5*x^2 + 0.041666666666666664*x^4 - 0.001388888888888889*x^6"
},
{
"id": 9,
"input": "gradient x^2 + y^2 + x*y",
"output": "d/dx = 2*x + y\nd/dy = 2*y + x"
}
]
}