How much RAM do you have? CivIV does choke on small amounts of RAM, especially zoomed-out, so that may be your problem. 512 MB on XP or 1024 MB on Vista is not really enough to run CivIV properly on larger than average maps. Integrated graphics exacerbate that problem, as they borrow RAM from the system to power the graphics. So if you have that much RAM, monitor it with Task Manager while playing, and if it's hitting the ceiling, you need to add more RAM for better performance.
Turning down settings such as Graphics Detail, Single Unit Animation, and other general animation settings should help. Also turn down/off antialiasing if it is on. Other than that, I can't think of anything. But if it's any consolation, 11 FPS is still much better than having several hundred megabytes too few of RAM.