#include <stdio.h>
#include <math.h>
#include <assert.h>

double simpson(double (*f)(double), double a, double b, int n);
double f(double);
double antider_f(double);

double f(double x) {
    // return x*x*x - x - 1.;
    return sin(x);
}

double antider_f(double x) {
    // return x*x*x*x/4. - x*x/2. - x;
    return (-cos(x));
}

int main() {
    double a, b;
    int n;
    while (true) {
        printf("a, b, n:\n");
        if (scanf("%lf%lf%d", &a, &b, &n) < 3 || n <= 0)
            break;
        double s = simpson(&f, a, b, n);
        double s0 = antider_f(b) - antider_f(a);
        printf("integral = %.12f\n", s);
        printf("must be:   %.12f\n", s0);
    }
    return 0;
}

double simpson(double (*f)(double), double a, double b, int n) {
    assert(n > 0);
    double h = (b - a)/n;
    double s1 = (*f)(a) + (*f)(b);
    double s2 = 0.;
    double x = a + h;
    for (int i = 0; i < n - 1; ++i) {
        s2 += (*f)(x);
        x += h;
    }
    double s4 = 0.;
    x = a + h/2.;    
    for (int i = 0; i < n; ++i) {
        s4 += (*f)(x);
        x += h;
    }
    return (s1 + 2.*s2 + 4.*s4)*h/6.;
}