template <typename F>
class IntegrationMethod {
public:
    virtual double Integrate(F func, double a, double b, int n) {}
};

template <typename F>
class RectangleRule : public IntegrationMethod<F> {
private:
    double result;
    double x1, x2;
public:
    double Integrate(F func, double a, double b, int n) {
        x2 = a;
        for (int i = 0; i < n; i++) {
            x1 = x2;
            x2 = a + ((b - a) / n) * (i + 1);
            result += func((x1 + x2) / 2) * (x2 - x1);
        }
        return result;
    }
};

template <typename F>
class TrapezoidalRule : public IntegrationMethod<F> {
public:
    double Integrate(F func, double a, double b, int n) {
        double result;
        double x1;
        double x2 = a;
        for (int i = 0; i < n; i++) {
            x1 = x2;
            x2 = a + ((b - a) / n) * (i + 1);
            result += ((func(x1) + func(x2)) / 2) * (x2 - x1);
        }
        return result;
    }
};

#include <cmath>
#include <iostream>
#include <memory>
#include <string>

int main() {
    using F = decltype(cos);

    std::string input;
    std::cin >> input;
    std::unique_ptr<IntegrationMethod<F>> method;
    if (input == "rectangle")
        method.reset(new RectangleRule<F>);
    else
        method.reset(new TrapezoidalRule<F>);

    double x, y;
    std::cin >> x >> y;

    int n;
    std::cin >> n;

    std::cout << method->Integrate(cos, x, y, n) << "\n";
    std::cout << method->Integrate(sin, x, y, n) << "\n";
}