Q: Car losing power, shaking, and sputtering.

Leaving the gas cap off wont usually cause drivability concerns. Its function is basically to keep fuel vapors where they belong. If left off it often triggers a check engine light, but nothing more. Notice how I said "usually" in the first sentence? On some vehicles it might trigger a limp home mode. Limp home means just that, the vehicle computer shuts off most of the power and gives you just enough to get home. This is enough to scare people into calling a technician. If your gas cap is still off, put one on. If its in limp home mode, it should reset after a couple of key cycles. If it is still acting up, the drivability concern is probably coincidental with you leaving the gas cap off. Seeking help from a properly trained technician to diagnose the issue should be your next step.