Battery Problems???
 

I have a manual 2005 Mazda 3. It has 40,000 miles on it. Yesterday I went to start my car and it wouldn't start. I could hear the starter going, so it seemed that the battery was the problem. I put a battery charger on it, and brought it from low charge to full and let it sit overnight. This afternoon I started the car... seemed to have no trouble starting. Then I was going to drive it to Batteries Plus to see if they could test my battery and possibly buy a new one. The drive to the store was a nightmare. Anytime I would come to a stop, my car had a VERY rough idle. To the point where it would die. I had to keep it in neutral and rev it at all the stop lights, but it died twice along the way. When I finally made it to the store, they tested my battery. It was at 400 (output???), and the recommended was 550, so I got a new battery. The car now starts just fine, but the idle is still rough. It seemed to get better the more I drove it. Is it possible that my car is just "relearning" the idle and other things that were reset when my battery was dead/disconnected to be replaced? Or do you think it has some other problem, like spark plugs/wires, etc? On a scale of 1 to 10, I am about a 3 when it comes to car engine knowledge, so any help would be appreciated. Thanks,

I doubt the two incidents are connected.
At 40k, I think I would do a tuneup and see if that corrects the problem. Spark plugs, wouldn't hurt to replace the plug wires, new fuel filter, air cleaner element. If it still does it after that, I think you are going to have to take it to a mechanic.