How do I fix this problem?

I have a concrete drive. One section of it (approx. 12' x 16') is
PERFECTLY level around the perimeter, but sags a little in the center,
which holds water. This means that when it rains it holds water in the
whole section. Yes, whoever installed it didn't do a very good job.

I thought about drilling a hole in hopes it would drain this section,
but I assume it would clog up in short order. I thought about cutting
out a trough to let the water escape, but think this would look tacky.
I don't want to go to the expense of replacing the section. Replacing
the section would be a different color and look like ****. The
driveway is about 200 ft long which would totally be out of my range
for replacing the whole drive way.

Got any suggestions?

TIA

Hank