import java.util.*;
import java.io.*;

public class Main {

    double A = 0;
    double B = Math.PI / 2;

    int[] steps = { 10, 20, 50, 100 };
    private void solve() {
        for (int s : steps) {
            System.out.printf("Simpson(%d) = %f\n", s, simpson(s, A, B));
        }
        for (int s = 3; s <= 7; ++s) {
            System.out.printf("Newton(%d) = %f\n", s, newton(s, A, B));
        }
    }

    private double newton(int steps, double a, double b) {
        double res = 0;
        double h = (b - a) / steps;
        for (int it = 0; it <= steps; ++it) {
            res += f(a + it * h) * H[steps][it];
        }
        return res * (b - a);
    }

    private double simpson(int steps, double a, double b) {
        double h = (b - a) / steps;
        double res = 0;
        for (int it = 0; it < steps; ++it) {
            res += f(a + it * h) + 4 * f(a + (it + 0.5) * h) + f(a + (it + 1) * h);
        }
        return res * h / 6;
    }

    private double f(double x) {
        return Math.sin(x);
    }

    double[][] H = new double[8][9];
    {
        H[1][0] = H[1][1] = 0.5;
        //
        H[2][0] = H[2][2] = 1.0 / 6;
        H[2][1] = 2.0 / 3;
        //
        H[3][0] = H[3][3] = 1.0 / 8;
        H[3][1] = H[3][2] = 3.0 / 8;
        //
        H[4][0] = H[4][4] = 7.0 / 90;
        H[4][1] = H[4][3] = 16.0 / 45;
        H[4][2] = 2.0 / 15;
        //
        H[5][0] = H[5][5] = 19.0 / 288;
        H[5][1] = H[5][4] = 25.0 / 96;
        H[5][2] = H[5][3] = 25.0 / 144;
        //
        H[6][0] = H[6][6] = 41.0 / 840;
        H[6][1] = H[6][5] = 9.0 / 35;
        H[6][2] = H[6][4] = 9.0 / 280;
        H[6][3] = 34.0 / 105;
        //
        H[7][0] = H[7][7] = 751.0 / 17280;
        H[7][1] = H[7][6] = 3577.0 / 17280;
        H[7][2] = H[7][5] = 1323.0 / 17280;
        H[7][3] = H[7][4] = 2989.0 / 17280;
    }

    public static void main(String[] argc) {
        new Main().solve();
    }
}