code: class NumericalIntegration
  {
  
    interface FPFunction
    {
      double eval(double n);
    }
  
    public static double rectangularLeft(double a, double b, int n, FPFunction f)
    {
      return rectangular(a, b, n, f, 0);
    }
  
    public static double rectangularMidpoint(double a, double b, int n, FPFunction f)
    {
      return rectangular(a, b, n, f, 1);
    }
  
    public static double rectangularRight(double a, double b, int n, FPFunction f)
    {
      return rectangular(a, b, n, f, 2);
    }
  
    public static double trapezium(double a, double b, int n, FPFunction f)
    {
      double range = checkParamsGetRange(a, b, n);
      double nFloat = (double)n;
      double sum = 0.0;
      for (int i = 1; i < n; i++)
      {
        double x = a + range * (double)i / nFloat;
        sum += f.eval(x);
      }
      sum += (f.eval(a) + f.eval(b)) / 2.0;
      return sum * range / nFloat;
    }
  
    public static double simpsons(double a, double b, int n, FPFunction f)
    {
      double range = checkParamsGetRange(a, b, n);
      double nFloat = (double)n;
      double sum1 = f.eval(a + range / (nFloat * 2.0));
      double sum2 = 0.0;
      for (int i = 1; i < n; i++)
      {
        double x1 = a + range * ((double)i + 0.5) / nFloat;
        sum1 += f.eval(x1);
        double x2 = a + range * (double)i / nFloat;
        sum2 += f.eval(x2);
      }
      return (f.eval(a) + f.eval(b) + sum1 * 4.0 + sum2 * 2.0) * range / (nFloat * 6.0);
    }
  
    private static double rectangular(double a, double b, int n, FPFunction f, int mode)
    {
      double range = checkParamsGetRange(a, b, n);
      double modeOffset = (double)mode / 2.0;
      double nFloat = (double)n;
      double sum = 0.0;
      for (int i = 0; i < n; i++)
      {
        double x = a + range * ((double)i + modeOffset) / nFloat;
        sum += f.eval(x);
      }
      return sum * range / nFloat;
    }
  
    private static double checkParamsGetRange(double a, double b, int n)
    {
      if (n <= 0)
        throw new IllegalArgumentException("Invalid value of n");
      double range = b - a;
      if (range <= 0)
        throw new IllegalArgumentException("Invalid range");
      return range;
    }
  
  
    private static void testFunction(String fname, double a, double b, int n, FPFunction f)
    {
      System.out.println("Testing function \"" + fname + "\", a=" + a + ", b=" + b + ", n=" + n);
      System.out.println("rectangularLeft: " + rectangularLeft(a, b, n, f));
      System.out.println("rectangularMidpoint: " + rectangularMidpoint(a, b, n, f));
      System.out.println("rectangularRight: " + rectangularRight(a, b, n, f));
      System.out.println("trapezium: " + trapezium(a, b, n, f));
      System.out.println("simpsons: " + simpsons(a, b, n, f));
      System.out.println();
      return;
    }
  
    public static void main(String[] args)
    {
      testFunction("x^3", 0.0, 1.0, 100, new FPFunction() {
          public double eval(double n) {
            return n * n * n;
          }
        }
      );
  
      testFunction("1/x", 1.0, 100.0, 1000, new FPFunction() {
          public double eval(double n) {
            return 1.0 / n;
          }
        }
      );
  
      testFunction("x", 0.0, 5000.0, 5000000, new FPFunction() {
          public double eval(double n) {
            return n;
          }
        }
      );
  
      testFunction("x", 0.0, 6000.0, 6000000, new FPFunction() {
          public double eval(double n) {
            return n;
          }
        }
      );
  
      return;
    }
  }
  