gh-128307: Support eager_start=<bool> in create_eager_task_factory and various create_task functions (#128306)

Some create_task() functions were changed from `name=None, context=None` to `**kwargs`.

Co-authored-by: Guido van Rossum <gvanrossum@gmail.com>

Lib/test/test_asyncio/test_tasks.py

@@ -89,8 +89,8 @@ class BaseTaskTests:
     Future = None
     all_tasks = None
 
-    def new_task(self, loop, coro, name='TestTask', context=None):
-        return self.__class__.Task(coro, loop=loop, name=name, context=context)
+    def new_task(self, loop, coro, name='TestTask', context=None, eager_start=None):
+        return self.__class__.Task(coro, loop=loop, name=name, context=context, eager_start=eager_start)
 
     def new_future(self, loop):
         return self.__class__.Future(loop=loop)
@@ -2686,6 +2686,35 @@ class BaseTaskTests:
 
         self.assertEqual([None, 1, 2], ret)
 
+    def test_eager_start_true(self):
+        name = None
+
+        async def asyncfn():
+            nonlocal name
+            name = self.current_task().get_name()
+
+        async def main():
+            t = self.new_task(coro=asyncfn(), loop=asyncio.get_running_loop(), eager_start=True, name="example")
+            self.assertTrue(t.done())
+            self.assertEqual(name, "example")
+            await t
+
+    def test_eager_start_false(self):
+        name = None
+
+        async def asyncfn():
+            nonlocal name
+            name = self.current_task().get_name()
+
+        async def main():
+            t = self.new_task(coro=asyncfn(), loop=asyncio.get_running_loop(), eager_start=False, name="example")
+            self.assertFalse(t.done())
+            self.assertIsNone(name)
+            await t
+            self.assertEqual(name, "example")
+
+        asyncio.run(main(), loop_factory=asyncio.EventLoop)
+
     def test_get_coro(self):
         loop = asyncio.new_event_loop()
         coro = coroutine_function()