#include <iostream>
#pragma warning ( disable : 4996)

using namespace std;

double Input()
{
    double Number;
    while (true)
    {
        printf("%s", "Write epsilon: ");
        scanf("%lf", &Number);
        if (Number > 0.1 || Number < 0.0000001)
        {
            printf("%s", "Incorrect epsilon, epsilon must be more then 10^(-7) and less then 10^(-1) try again...\n");
        }
        else
        {
            return Number;
        }
    }
}

double func1(double x)
{
    return x * sqrt(1 + x);
}

double func2(double x)
{
    return asin(sqrt(x)) / sqrt(x * (1 - x));
}

double func3(double x)
{
    return pow(2, x) / (1 + pow(4, x));
}

double integral(double func(double(x)), double left_border, double right_border, long long num_of_divizions)
{
    double area = 0, height = abs((right_border - left_border) / num_of_divizions);
    for (long long i = 0; i < num_of_divizions; i++)
    {
        area += ((func(left_border) + func(left_border + height)) / 2) * height;
        left_border += height;
    }
    return area;
}

double integral(double func(double), double left_border, double right_border, double epsilon)
{
    int sign = 1;
    if (left_border > right_border)
    {
        swap(right_border, left_border);
        sign = -1;
    }
    double actual_area;
    double next_area;
    long long i = 2;
    while (true)
    {
        actual_area = integral(func, left_border, right_border, i);
        next_area = integral(func, left_border, right_border, i * 2);
        if (abs(actual_area - next_area) <= epsilon)
        {
            printf("Number of divizions: %lld %c", i * 2, '\n');
            return next_area * sign;
        }
        i*=2;
    }
}

int main()
{
    double epsilon;
    epsilon = Input();
    printf("%s %lf %c", "Integral of func #1: ", integral(&func1, 2, 7, epsilon), '\n');
    printf("%s %lf %c", "Integral of func #2: ", integral(&func2, 0.2, 0.3, epsilon), '\n');
    printf("%s %lf %c", "Integral of func #3: ", integral(&func3, -13, -2, epsilon), '\n');
}