I recently had an electrician come in to run power to a staircase that
was dark. In order to extend the power, he had to cut several circular
holes in the drywall or the ceiling to reach the existing power. He
left behind the holes he cut, so in theory it should be easy to replace
the hole, but I'm struggling with how to patch the holes in the
ceiling.

I tried just using spackle/paste around the edges, but the problem I
ran into was that it was difficult to keep the hole piece flat and
flush with the existing ceiling. How can I patch this effectively?

Many thanks in advance....

--charlie