At 35 to 45 Watts you'll want more runtime (mah) as you would be well below the amp limits of majority of the batteries out there, the three models best for that runtime would be
The Samsung 30Q 3000mah, (Manufacturer rated at 15amps but Mooch has tested them and they can handle 20amps just fine, so you have some wiggle room up to about 60watts max)
The LG HG2 3000mah (Manufacturer rated 20amp, tested by Mooch about 18amps max, like the 30Q occasionally can be wiggled up to max 60watts)
The Sony VTC6 3000mah (Manufacturer rated 15amps like the 30Q, tested by Mooch 19amps Max, like the 30Q and HG2 max watts 60watts, these are pricier than the other 2 models, but they also hold voltage longer in the 3.7 to 3.9v median charge plateau and have less voltage sag)
75watts you really need 25amp Batteries which there are 4 Models
Highest Suggested is the Sony VTC5A (take note of the "A" as there is an older VTC5 2600mah that is only 20amps, the 5A has 5 more amps for a total of 25amps over its older brother, they are hard to find and pricey due their popularity)
LG has the HD2, HD2C, and HD4, and all are very nice 25amp batteries though their Mah ratings are in the 2000 to 2200mah range, where the previous VTC5A is in the 2500 to 2600mah rating range, if want to save some money the LG's will work just fine in the 75watts category for you.