async def METHOD_NAME(anyio_backend: str) -> None:
    provider = Provide(dependency=async_callable, use_cache=True)
    assert provider.value is Empty
    value = await provider()
    assert value == "three-one"
    assert provider.value == value
    second_value = await provider()
    assert value == second_value
    third_value = await provider()
    assert value == third_value