TaskExtensions.cs

using System;
using System.Threading.Tasks;

public static class TaskExtensions
{
    public delegate void ExceptionCallback(Exception exception);
    public delegate void CompleteCallback<in T>(T result);
    public delegate void CompleteCallback();
    
    public static Task<T> WithResult<T>(this Task task, Func<Task, T> func) => 
        task.ContinueWith<T>(func);
    public static Task<T> WithResult<T>(this Task task, Func<T> func) => 
        task.WithResult<T>(t => func());
    public static Task<T> WithResult<T>(this Task task, T value = default) => 
        task.WithResult(_ => value);

    public static Task WithException(this Task task, Exception exception) =>
        task.WithResult<object>().WithException(exception);
    
    public static async Task<T> WithException<T>(this Task<T> task, Exception exception)
    {
        await task;
        throw exception;
    }

    public static void Forget(this Task task, 
        CompleteCallback completeCallback = null, 
        ExceptionCallback exceptionCallback = null) =>
        task.WithResult<object>().Forget(
            _ => completeCallback?.Invoke(), 
            exceptionCallback);

    public static void Forget<T>(this Task<T> task, 
        CompleteCallback<T> completeCallback = null,
        ExceptionCallback exceptionCallback = null) =>
        task.Subscribe(completeCallback, exceptionCallback);

    public static Task Subscribe(this Task task,
        CompleteCallback completeCallback = null,
        ExceptionCallback exceptionCallback = null) =>
        task.WithResult<object>().Subscribe(
            _ => completeCallback?.Invoke(),
            exceptionCallback);
    
    public static Task<T> Subscribe<T>(this Task<T> task,
        CompleteCallback<T> completeCallback = null, 
        ExceptionCallback exceptionCallback = null) =>
        task.ContinueWith(t =>
        {
            if(t.IsFaulted)
                exceptionCallback?.Invoke(t.Exception);
            else if (t.IsCompleted)
            {
                completeCallback?.Invoke(t.Result);
                return t.Result;
            }

            return default;
        });
}