Feeding these guys is really, really simple.
Cucumber might work, but it's probably not the best place to start. Mystery snails (Pomacea Bridgesii) do not feed on live plants or fresh vegetables. They eat only dead or decaying plant matter. Therefore it's important to give them slightly cooked veggies, not fresh ones. The best way to do this is to microwave the veggies in a wet paper towel for 10 or 15 seconds, or to blanch the veggies. This way your snail can start eating right away, rather than waiting for the food to decay for a few days before eating it.
While they will eat cucumber, a better choice would be romaine lettuce, collard greens, spinach, or parsley. These are high-calcium vegetables that will promote a strong, healthy shell.
Even more important than the food is water quality. Clean, low-ammonia, low-nitrite water with a high pH and kH, and rich in calcium.
I highly recommend that you check out applesnail.net. It has everything you need to know about raising a healthy snail. In fact, here's the quick and dirty guide to healthy snails:
http://applesnail.net/content/various/quick_guide.htm
But definitely check out the main site. It has much more information. You can join the forum (under Discussions) for even more info. We're a very friendly bunch.