Schedule tasks which are futures to completion (#112269)

packages/flutter/lib/src/scheduler/binding.dart

@@ -50,7 +50,7 @@ typedef FrameCallback = void Function(Duration timeStamp);
 ///
 /// The type argument `T` is the task's return value. Consider `void` if the
 /// task does not return a value.
-typedef TaskCallback<T> = T Function();
+typedef TaskCallback<T> = FutureOr<T> Function();
 
 /// Signature for the [SchedulerBinding.schedulingStrategy] callback. Called
 /// whenever the system needs to decide whether a task at a given
@@ -409,8 +409,12 @@ mixin SchedulerBinding on BindingBase {
   }
   final PriorityQueue<_TaskEntry<dynamic>> _taskQueue = HeapPriorityQueue<_TaskEntry<dynamic>>(_taskSorter);
 
-  /// Schedules the given `task` with the given `priority` and returns a
+  /// Schedules the given `task` with the given `priority`.
-  /// [Future] that completes to the `task`'s eventual return value.
+  ///
+  /// If `task` returns a future, the future returned by [scheduleTask] will
+  /// complete after the former future has been scheduled to completion.
+  /// Otherwise, the returned future for [scheduleTask] will complete with the
+  /// same value returned by `task` after it has been scheduled.
   ///
   /// The `debugLabel` and `flow` are used to report the task to the [Timeline],
   /// for use when profiling.

packages/flutter/test/scheduler/scheduler_test.dart

@@ -250,6 +250,31 @@ void main() {
     warmUpDrawFrame();
     expect(scheduler.hasScheduledFrame, isTrue);
   });
+
+  test('Can schedule futures to completion', () async {
+    bool isCompleted = false;
+
+    // `Future` is disallowed in this file due to the import of
+    // scheduler_tester.dart so annotations cannot be specified.
+    // ignore: always_specify_types
+    final result = scheduler.scheduleTask(
+      () async {
+        // Yield, so if awaiting `result` did not wait for completion of this
+        // task, the assertion on `isCompleted` will fail.
+        await null;
+        await null;
+
+        isCompleted = true;
+        return 1;
+      },
+      Priority.idle,
+    );
+
+    scheduler.handleEventLoopCallback();
+    await result;
+
+    expect(isCompleted, true);
+  });
 }
 
 class DummyTimer implements Timer {