#include <iostream>
#include <cmath>
#include <cstdio>
#include <cstdlib>

typedef double(*function)(double);

double integral(function f, double a, double b, unsigned step_count) {
    double sum = .0, step;
    size_t i;
    if (0 == step_count) return sum;

    step = (b - a) / (1.0 * step_count);
    for (i = 1; i < step_count; ++i) {
        sum += f(a + i * step);
    }
    sum += (f(a) + f(b)) / 2;
    sum *= step;
    return sum;
}

double f(double x) {
    return 2 + pow(x, 3);
}

double simpsonIntegral(double a, double b, int n, function f) {
    const double width = (b - a) / n;

    double simpson_integral = 0;
    for (int step = 0; step < n; step++) {
        const double x1 = a + step * width;
        const double x2 = a + (step + 1) * width;

        simpson_integral += (x2 - x1) / 6.0 * (f(x1) + 4.0 * f(0.5 * (x1 + x2)) + f(x2));
    }

    return simpson_integral;
}

int main() {
    printf("\ResultTRAP = %f\n", integral(f, 8, 14, 200));
    printf("\ResultPARA = %f\n", simpsonIntegral(8, 14, 200, f));
}