Engine stalling when decelerating
 

Hi new to the group, I would greatly appreciate any advice that anyone can offer. I drive a 2005 Mazda 3 sedan and so far I have had very few problems.
This Monday I went to start my car and my battery had died, and I had it replaced.
When I went to drive my car the next day I noticed that the RPM’s where idling very high, and when I drive my car it feels like it is laboring harder than it should.
The biggest problem is that when I decelerate the engine shuts off and I have to restart it. Particularly if I apply the break.
I took it to my mechanic twice and he claims there is nothing wrong with it because it did not trip off any codes and that I just need to let it warm up. But on my way home it stalled three times! Twice after it had fully warmed up.
If anybody has any idea what is wrong with it I would greatly appreciate it so that I can help explain the problem to my (new) mechanic when I bring it in.

Thanks.

one more thing.

I noticed just now while driving at night that the head lights flicker from bright to dim with the engine when it is revving.

My daughter is having the same issue with the same car. When the car is coming to a stop its idle becomes uneven and will stall if you don't play with the accelerator. She also noted the thermostat had fluctuated to cold and back to normal after the car was warmed up. I've researched other threads and got answers from faulty thermostat, dirty throttle body, purge solenoid. I might call mazda to see if there are any bulletins out on this problem.