2001 Buick Regal stalls out

2001 Buick Regal mileage: 42,000. The first sign of trouble was while driving with the cruise control on. Suddenly, the cruise cut off, and the car de-accelerated as if it were going to stall out. It didn't, and the car continued to run just fine, but I didn't try turn on the cruise control again. Then, at the end of this same trip, in a parking lot, the car began to sort-of buck and surge as I was braking, but not until I slowed to about 40 MPH and below. Next, I was driving at about 40-50 MPH and the car cut off twice. Since then, the car has been OK, but I have been driving very gently, and the only symptom at this point is that as I approach idle while braking, the car surges and bucks a little bit, as if it is either a) not getting a continuous flow of gas, or b) having trouble coordinating downshifting and running at the same time. The car has an automatic transmission; unfortunately, I don't know the engine type. I think it is a 6-cylinder engine.