Hi all
I have a Nissan Maxima 1999, this car was working nice but since a few days this is happening sometimes when I press the brake or I redused the speed the engine shut off, but when I turn it on It turns nicely, the muffler exhaust a lot of smoke that smells like stool water when I turn it back on, but them it starts again, it doesn’t happen to me all the time, sometimes happened with the fuel tank full or empty, I took it to valvoline and they changed all the oil and told me everything was fine the only problem they found was the serpentine belt it was damaged! Please help 
I think you have a couple of problems.
I think the engine shutting off when you step on the brakes and sometimes when you decelerate is being caused by a leak in the brake booster. You can test for this by clamping off the booster check valve tube and seeing of the engine responds differently when stepping on the brakes… but do NOT try to drive it this way on the streets unless you’re prepared to stop safely without the booster’s assistance.
I suspect your engine is burning much oil, and possibly other fluids like coolant. You need to get this looked at ASAP. Is there yellow goop stuck to the bottom of the oil fill cap? Have you been losing coolant? Has the engine been overheating?
Can you describe the damage? Was the belt oil soaked? Coolant soaked? Way too old?
We can attempt to help you find the solutions over this forum, but in all honesty I think this vehicle needs a really good once-over. I suspect you have more going on here than your post suggests.
Concur w/TSB above on the first point, most likely a defective brake booster. The second problem, the black smoke out the tailpipe, that could be caused by the brake booster too. In some cases a failed brake booster will allow brake fluid to be drawn into the intake manifold, and that creates a lot of exhaust smoke. Suggest to check the brake fluid level asap as if the brake fluid has been sucked into the engine, the fluid level might be very low.