Folks have touched on this, but I thought summarizing it directly might help(I'm dusting off my physics minor here):
3000 mAH means: You can pull 3000 mA out of the battery for one hour, and then it's dead.
The problem is that mA is meaningless without volts.
The amount of usable energy that can be pulled from a battery needs to be measured in watt hours. There's an equation for watts:
Watts = Amps(mA in this case) x Volts (to get from watts to watt hours, you just multiply by the number of hours that the battery can support those amps for. So a 1 volt battery that can support 1 amp for 1 hour, is a one-watt-hour battery. A 1 volt battery that can support 1 amp for 5 hours, is a 5 watt-hour-battery)
As an example:
Let's say a battery (#1) can support 3000 mA for 1 hour at 5 volts. (15 watt hours) A second battery (#2) can support 3000 mA for 1 hour at 10 volts, which supplies twice as much energy (30 watt hours). Conversely, if the voltage goes down: a battery (#3) that goes dead after 3000 mA for 1 hour at 1 volt can only supply 1/5 the energy (3 watt hours) of battery #1.
I know I'm repeating myself: mAH is meaningless without volts. 3000mAH at 120 volts is a lot of power (in this context anyway). 3000mAH at .5 volts is very little power at all. Same mAH, but very different stored energy. If you want to compare the usable energy in different batteries, you have to figure out what the watt hours are.
3000 mAH means: You can pull 3000 mA out of the battery for one hour, and then it's dead.
The problem is that mA is meaningless without volts.
The amount of usable energy that can be pulled from a battery needs to be measured in watt hours. There's an equation for watts:
Watts = Amps(mA in this case) x Volts (to get from watts to watt hours, you just multiply by the number of hours that the battery can support those amps for. So a 1 volt battery that can support 1 amp for 1 hour, is a one-watt-hour battery. A 1 volt battery that can support 1 amp for 5 hours, is a 5 watt-hour-battery)
As an example:
Let's say a battery (#1) can support 3000 mA for 1 hour at 5 volts. (15 watt hours) A second battery (#2) can support 3000 mA for 1 hour at 10 volts, which supplies twice as much energy (30 watt hours). Conversely, if the voltage goes down: a battery (#3) that goes dead after 3000 mA for 1 hour at 1 volt can only supply 1/5 the energy (3 watt hours) of battery #1.
I know I'm repeating myself: mAH is meaningless without volts. 3000mAH at 120 volts is a lot of power (in this context anyway). 3000mAH at .5 volts is very little power at all. Same mAH, but very different stored energy. If you want to compare the usable energy in different batteries, you have to figure out what the watt hours are.