The Ikea "Sunnan" solar powered LED desk lamp. ( $20 )
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This is a very cool and useful desk lamp / work lamp. Simply pop the battery pack out, put it in a sunny place during the day. When the sun does down, snap the battery in the base. Base Cost : $20 High Capacity NiMH : $12 ( 4 pack, only need 3 ) Charge time : suggested - 9-12 hours, actual - still testing Run time : suggested - 3 hours, actual - still testing

http://www.ikea.com/us/en/catalog/products/90154371

How do I replace the NiMH rechargeable 1.2v 1200mAh batteries with high capacity ones?
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Unscrew the 4 screws on the bottom of the battery pack / solar cell
Flip the pack upright
The top, solar cell, will be loose
Flip over the solar cell. You now have access to the rechargeable batteries. The original NiMH 1.2v 1200mAh can be replaced with high capacity NiMH. You can see that the 3 batteries are connected in series. This will give the required 3.6v that is needed by the white LED's.