Task: Numerical integration
C#: using System;
using System.Collections.Generic;
using System.Linq;

public class Interval
{
    public Interval(double leftEndpoint, double size)
    {
        LeftEndpoint = leftEndpoint;
        RightEndpoint = leftEndpoint + size;
    }

    public double LeftEndpoint
    {
        get;
        set;
    }

    public double RightEndpoint
    {
        get;
        set;
    }

    public double Size
    {
        get
        {
            return RightEndpoint - LeftEndpoint;
        }
    }

    public double Center
    {
        get
        {
            return (LeftEndpoint + RightEndpoint) / 2;
        }
    }

    public IEnumerable<Interval> Subdivide(int subintervalCount)
    {
        double subintervalSize = Size / subintervalCount;
        return Enumerable.Range(0, subintervalCount).Select(index => new Interval(LeftEndpoint + index * subintervalSize, subintervalSize));
    }
}

public class DefiniteIntegral
{
    public DefiniteIntegral(Func<double, double> integrand, Interval domain)
    {
        Integrand = integrand;
        Domain = domain;
    }

    public Func<double, double> Integrand
    {
        get;
        set;
    }

    public Interval Domain
    {
        get;
        set;
    }

    public double SampleIntegrand(ApproximationMethod approximationMethod, Interval subdomain)
    {
        switch (approximationMethod)
        {
            case ApproximationMethod.RectangleLeft:
                return Integrand(subdomain.LeftEndpoint);
            case ApproximationMethod.RectangleMidpoint:
                return Integrand(subdomain.Center);
            case ApproximationMethod.RectangleRight:
                return Integrand(subdomain.RightEndpoint);
            case ApproximationMethod.Trapezium:
                return (Integrand(subdomain.LeftEndpoint) + Integrand(subdomain.RightEndpoint)) / 2;
            case ApproximationMethod.Simpson:
                return (Integrand(subdomain.LeftEndpoint) + 4 * Integrand(subdomain.Center) + Integrand(subdomain.RightEndpoint)) / 6;
            default:
                throw new NotImplementedException();
        }
    }

    public double Approximate(ApproximationMethod approximationMethod, int subdomainCount)
    {
        return Domain.Size * Domain.Subdivide(subdomainCount).Sum(subdomain => SampleIntegrand(approximationMethod, subdomain)) / subdomainCount;
    }

    public enum ApproximationMethod
    {
        RectangleLeft,
        RectangleMidpoint,
        RectangleRight,
        Trapezium,
        Simpson
    }
}

public class Program
{
    private static void TestApproximationMethods(DefiniteIntegral integral, int subdomainCount)
    {
        foreach (DefiniteIntegral.ApproximationMethod approximationMethod in Enum.GetValues(typeof(DefiniteIntegral.ApproximationMethod)))
        {
            Console.WriteLine(integral.Approximate(approximationMethod, subdomainCount));
        }
    }

    public static void Main()
    {
        TestApproximationMethods(new DefiniteIntegral(x => x * x * x, new Interval(0, 1)), 10000);
        TestApproximationMethods(new DefiniteIntegral(x => 1 / x, new Interval(1, 99)), 1000);
        TestApproximationMethods(new DefiniteIntegral(x => x, new Interval(0, 5000)), 500000);
        TestApproximationMethods(new DefiniteIntegral(x => x, new Interval(0, 6000)), 6000000);
    }
}

Java: 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;
  }
}