Task: Active object
Java: 
public class Integrator {

    public interface Function {
        double apply(double timeSinceStartInSeconds);
    }

    private final long start;
    private volatile boolean running;

    private Function func;
    private double t0;
    private double v0;
    private double sum;

    public Integrator(Function func) {
        this.start = System.nanoTime();
        setFunc(func);
        new Thread(this::integrate).start();
    }

    public void setFunc(Function func) {
        this.func = func;
        v0 = func.apply(0.0);
        t0 = 0;
    }

    public double getOutput() {
        return sum;
    }

    public void stop() {
        running = false;
    }

    private void integrate() {
        running = true;
        while (running) {
            try {
                Thread.sleep(1);
                update();
            } catch (InterruptedException e) {
                return;
            }
        }
    }

    private void update() {
        double t1 = (System.nanoTime() - start) / 1.0e9;
        double v1 = func.apply(t1);
        double rect = (t1 - t0) * (v0 + v1) / 2;
        this.sum += rect;
        t0 = t1;
        v0 = v1;
    }

    public static void main(String[] args) throws InterruptedException {
        Integrator integrator = new Integrator(t -> Math.sin(Math.PI * t));
        Thread.sleep(2000);

        integrator.setFunc(t -> 0.0);
        Thread.sleep(500);

        integrator.stop();
        System.out.println(integrator.getOutput());
    }
}

VB: Module Module1
 
    Sub Main()
        Using active As New Integrator
            active.Operation = Function(t As Double) Math.Sin(2 * Math.PI * 0.5 * t)
            Threading.Thread.Sleep(TimeSpan.FromSeconds(2))
            Console.WriteLine(active.Value)
            active.Operation = Function(t As Double) 0
            Threading.Thread.Sleep(TimeSpan.FromSeconds(0.5))
            Console.WriteLine(active.Value)
        End Using
        Console.ReadLine()
    End Sub
 
End Module
  
Class Integrator
    Implements IDisposable
 
    Private m_Operation As Func(Of Double, Double)
    Private m_Disposed As Boolean
    Private m_SyncRoot As New Object
    Private m_Value As Double
 
    Public Sub New()
        m_Operation = Function(void) 0.0
        Dim t As New Threading.Thread(AddressOf MainLoop)
        t.Start()
    End Sub
 
    Private Sub MainLoop()
        Dim epoch = Now
        Dim t0 = 0.0
        Do
            SyncLock m_SyncRoot
                Dim t1 = (Now - epoch).TotalSeconds
                m_Value = m_Value + (Operation(t1) + Operation(t0)) * (t1 - t0) / 2
                t0 = t1
            End SyncLock
            Threading.Thread.Sleep(10)
        Loop Until m_Disposed
    End Sub
 
    Public Property Operation() As Func(Of Double, Double)
        Get
            SyncLock m_SyncRoot
                Return m_Operation
            End SyncLock
        End Get
        Set(ByVal value As Func(Of Double, Double))
            SyncLock m_SyncRoot
                m_Operation = value
            End SyncLock
        End Set
    End Property
 
    Public ReadOnly Property Value() As Double
        Get
            SyncLock m_SyncRoot
                Return m_Value
            End SyncLock
        End Get
    End Property
 
    Protected Overridable Sub Dispose(ByVal disposing As Boolean)
        m_Disposed = True
    End Sub
 
    Public Sub Dispose() Implements IDisposable.Dispose
        Dispose(True)
        GC.SuppressFinalize(Me)
    End Sub
 
End Class