03 Civic starts and drives fine then starts to stall of you give it too much gas. Back off the accelerator and sometimes it's fine sometimes drops idle and dies .Starts right back up usually. Other times have to wait 5 min. but then starts. Car sometimes makes it a to b just fine. Other times driving normal and out of nowhere or while slowing down to come to a stop dies. The check engine light is not on but "maintenance required" is on.

 

OK, I'll bite.

My guess is your fuel pump is failing. At low RPMs the fuel pump can pump enough fuel to keep the engine running. But at higher RPMs the pump can't keep up with the demand and the lack of fuel causes the engine to stall.

I would do a pressure check and watch not only what the final pressure is but how fast it gets there.

Or you could roll the dice, skip the pressure test and replace the fuel pump. The symptoms you've listed strongly indicate a bad fuel pump.

Disclaimer: I write software for a living and turn wrenches because I haven't found a mechanic I trust.

 

Check engine light? Get us some codes, there's no way that's happening without a cel