My second cell phone, a CDMA/IS54 device, used a large NiMH battery, and would hold charge for two days or so, if left on and intermittently used. I purchased it in 1999.
My current cell phone, a "tri-mode" device, uses a small NiMH battery, and will hold charge for almost five days if left on and intermittently used. I purchased it in 2002.
If Starfleet can't come up with a better battery than Nokia, it need to hire better engineers.
Well, consider that starfleet put warp engines in pods on the end of tiny sticks to push a huge dish full of people from 0 to Warp 6 in a few seconds.
Never could figure out why the engines didn't just rip themselves off and go flying through subspace on their own.
But I maintain that the communicators were recharged with solar power or methane gas (the were worn on the backside after al). They needed more power than your Nokia phone to reach the ship in orbit.
Shalom.