#include <iostream>
#include <cmath>
#include <string>
#include <stdexcept>

using namespace std;

double f(double x) {
    return sin(x); // Интегрируемая функция
}

double compute_integral(double a, double b, double epsilon, string method) {
    if (method == "left" || method == "right") {
        int n = 1;
        double h = (b - a) / n;
        double sum;
        if (method == "left") {
            sum = f(a);
        } else { // right
            sum = f(a + h); // Правая точка первого интервала
        }
        double integral = sum * h;
        double prev_integral;
        do {
            prev_integral = integral;
            n *= 2;
            h /= 2;
            double new_sum = 0.0;
            for (int i = 0; i < n / 2; ++i) {
                double x = a + (2 * i + 1) * h; // Середины предыдущих интервалов
                new_sum += f(x);
            }
            sum += new_sum;
            integral = sum * h;
        } while (abs(integral - prev_integral) > epsilon);
        return integral;
    } else if (method == "trapezoid") {
        int n = 1;
        double h = (b - a) / n;
        double S = 0.0; // Сумма внутренних точек
        double integral = (h / 2) * (f(a) + f(b));
        double prev_integral;
        do {
            prev_integral = integral;
            n *= 2;
            h /= 2;
            double sum_new = 0.0;
            for (int i = 0; i < n / 2; ++i) {
                double x = a + (2 * i + 1) * h;
                sum_new += f(x);
            }
            S += sum_new;
            integral = h * (0.5 * (f(a) + f(b)) + S);
        } while (abs(integral - prev_integral) > epsilon);
        return integral;
    } else if (method == "simpson") {
        if (b == a) return 0.0;
        int n = 2;
        double h = (b - a) / n;
        double sum_odd = f(a + h);
        double sum_even = 0.0;
        double integral = (h / 3) * (f(a) + 4 * sum_odd + f(b));
        double prev_integral;
        do {
            prev_integral = integral;
            n *= 2;
            h /= 2;
            double sum_odd_new = 0.0;
            for (int i = 0; i < n / 2; ++i) {
                double x = a + (2 * i + 1) * h;
                sum_odd_new += f(x);
            }
            sum_even += sum_odd;
            sum_odd = sum_odd_new;
            integral = (h / 3) * (f(a) + 2 * sum_even + 4 * sum_odd + f(b));
        } while (abs(integral - prev_integral) > epsilon);
        return integral;
    } else {
        throw invalid_argument("Unknown method");
    }
}

int main() {
    double a, b, epsilon;
    string method;
    cout << "Enter a: ";
    cin >> a;
    cout << "Enter b: ";
    cin >> b;
    cout << "Enter epsilon: ";
    cin >> epsilon;
    cout << "Enter method (left, right, trapezoid, simpson): ";
    cin >> method;

    try {
        double result = compute_integral(a, b, epsilon, method);
        cout << "Integral result: " << result << endl;
    } catch (const invalid_argument& e) {
        cerr << "Error: " << e.what() << endl;
    }

    return 0;
}