#include <iostream>
#include <iomanip>
#include <utility>
#include <cmath>

double f(double x);
double antider_f(double x);

double intergal_rect(
    double (*f)(double), double a, double b,
    double h = 0.001
);

double intergal_trap(
    double (*f)(double), double a, double b,
    double h = 0.001
);

double intergal_simpson(
    double (*f)(double), double a, double b,
    double h = 0.001
);

int main() {
    while (true) {
        std::cout << "Enter a, b:" << std::endl;
        double a, b;
        std::cin >> a >> b;
        if (!std::cin.good())
            break;
        std::cout << "Enter step size h:" << std::endl;
        double h;
        std::cin >> h;
        
        double int_rect = intergal_rect(&f, a, b, h);
        double integral = antider_f(b) - antider_f(a);
        std::cout << std::fixed << std::setprecision(14);
        std::cout << "Integral (rectangles) = " << int_rect << std::endl; 
        std::cout << "Integral (presize)    = " << integral << std::endl; 
        std::cout << "Error: " << fabs(int_rect - integral) << std::endl;

        double int_trap = intergal_trap(&f, a, b, h);
        std::cout << "Integral (trap.)   = " << int_trap << std::endl; 
        std::cout << "Integral (presize) = " << integral << std::endl; 
        std::cout << "Error: " << fabs(int_trap - integral) << std::endl;
    }
    return 0;
}      
    
double f(double x) {
    return x*x*x;
}

double antider_f(double x) {
    return x*x*x*x/4.;
}
    
double intergal_rect(
    double (*f)(double), double a, double b,
    double h /* = 0.001 */
) {
    double factor = 1.;
    if (b < a) {
        std::swap(a, b);
        factor = (-1.);
    }
        
    int n = int((b - a)/h);
    if (n == 0)
        n = 1;
    double dx = (b - a)/n;
    
    double s = 0.;
    double x = a;
    for (int i = 0; i < n; ++i) {
        s += (*f)(x);
        x += dx;
    }
    s *= dx;
    return s*factor;
}    

double intergal_trap(
    double (*f)(double), double a, double b,
    double h /* = 0.001 */
) {
    // To do...

    return 0.;
}

double intergal_simpson(
    double (*f)(double), double a, double b,
    double h /* = 0.001 */
) {
    // To do...

    return 0.;
}