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);
    }
}

C++: #include <atomic>
#include <chrono>
#include <cmath>
#include <iostream>
#include <mutex>
#include <thread>

using namespace std::chrono_literals;

class Integrator
{
  public:
    using clock_type = std::chrono::high_resolution_clock;
    using dur_t      = std::chrono::duration<double>;
    using func_t     = double(*)(double);

    explicit Integrator(func_t f = nullptr);
    ~Integrator();
    void input(func_t new_input);
    double output() { return integrate(); }

  private:
    std::atomic_flag continue_;
    std::mutex       mutex;
    std::thread      worker;

    func_t                       func;
    double                       state = 0;
    
    clock_type::time_point const beginning = clock_type::now();
    clock_type::time_point       t_prev = beginning;

    void do_work();
    double integrate();
};

Integrator::Integrator(func_t f) : func(f)
{
    continue_.test_and_set();
    worker = std::thread(&Integrator::do_work, this);
}

Integrator::~Integrator()
{
    continue_.clear();
    worker.join();
}

void Integrator::input(func_t new_input)
{
    integrate();
    std::lock_guard<std::mutex> lock(mutex);
    func = new_input;
}

void Integrator::do_work()
{
    while (continue_.test_and_set()) {
        integrate();
        std::this_thread::sleep_for(1ms);
    }
}

double Integrator::integrate()
{
    std::lock_guard<std::mutex> lock(mutex);
    auto now = clock_type::now();
    dur_t start = t_prev - beginning;
    dur_t fin   =    now - beginning;
    if (func)
        state += (func(start.count()) + func(fin.count())) * (fin - start).count() / 2;
    t_prev = now;
    return state;
}

double sine(double time)
{
    constexpr double PI = 3.1415926535897932;
    return std::sin(2 * PI * 0.5 * time);
}

int main()
{
    Integrator foo(sine);
    std::this_thread::sleep_for(2s);
    foo.input(nullptr);
    std::this_thread::sleep_for(500ms);
    std::cout << foo.output();
}