Souper Man,
Rechargable batteries are rated in mAh, which is milli-amp hours, not mA. They can deliver 20A (20,000mA) or more for some seconds.
Your 1800mAh battery cells can supply 180mA for 10 hours and maybe 1A for 1 hour when fully charged.
New solar garden lights use a single 1.2V Ni-Cad battery cell, a small 2V solar cell, very efficient LEDs and a voltage stepup circuit.