Task: Active object
C#: using System;
using System.Threading.Tasks;

using static System.Diagnostics.Stopwatch;
using static System.Math;
using static System.Threading.Thread;

class ActiveObject
{
    static double timeScale = 1.0 / Frequency;

    Func<double, double> func;
    Task updateTask;
    double integral;
    double value;
    long timestamp0, timestamp;

    public ActiveObject(Func<double, double> input)
    {
        timestamp0 = timestamp = GetTimestamp();
        func = input;
        value = func(0);
        updateTask = Integrate();
    }

    public void ChangeInput(Func<double, double> input)
    {
        lock (updateTask)
        {
            func = input;
        }
    }

    public double Value
    {
        get
        {
            lock (updateTask)
            {
                return integral;
            }
        }
    }

    async Task Integrate()
    {
        while (true)
        {
            await Task.Yield();
            var newTime = GetTimestamp();
            double newValue;

            lock (updateTask)
            {
                newValue = func((newTime - timestamp0) * timeScale);
                integral += (newValue + value) * (newTime - timestamp) * timeScale / 2;
            }

            timestamp = newTime;
            value = newValue;
        }
    }
}

class Program
{
    static Func<double, double> Sine(double frequency) =>
        t => Sin(2 * PI * frequency * t);

    static void Main(string[] args)
    {
        var ao = new ActiveObject(Sine(0.5));
        Sleep(TimeSpan.FromSeconds(2));
        ao.ChangeInput(t => 0);
        Sleep(TimeSpan.FromSeconds(0.5));
        Console.WriteLine(ao.Value);
    }
}

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