What is the ruling on someone who breaks their fast according to the Umm al-Qura calendar while the muezzin has not yet called the Adhan?

As long as the breaking of the fast occurred after the time for it began according to the calendar, there is no blame, and the fast is valid. This is because breaking the fast is tied to sunset, not to the call of the muezzin. Whenever a Muslim is certain or strongly believes that the sun has set, he is permitted to break his fast.