What I had been doing:

I have had an HP-49g+ for a while now, and have been using rechargeable AAA alkaline batteries in it almost as long as I've had it. While I was happy with how long the batteries would last, I found that I'd get the low battery warnings at the most annoying time (days when I'm using it constantly) and I was often away from my recharger and a spare set.

The problem:

Since my source for the rechargeable alkalines was gone, I was contemplating switching to NI-MH chemistry batteries. The NI-MH chargers I could find wanted to charge an even number of batteries, which meant that if I wanted to have a "ready" set, I would need to have a minimum of 9 (so effectively 12) batteries dedicated to powering my calculator (which of course runs off 3).

The idea:

Looking at my Motorola RAZR cell phone charging off a standard USB A to mini-B usb cable connected to my computer, I realized there must be an easier (and not so much more expensive way).

The RAZR has a USB mini-b connector and uses the 5V power available from the USB bus to charge it's lithium polymer battery. The HP-49g+ also has a USB mini-b connector, so if I could add a lithium polymer battery, it would be pretty handy (carry one cable, charge either device almost anywhere, any time).

planning:

space:

I've seen that many people have opened up their 49g+ to look inside, so I did the same thing. I found that a old credit card worked well to pry the bottom off, without scratcing the paint. After opening the calculator, I found that, with the exception of the battery holder, the bottom of the calculator case was empty, with plenty of room for a compact battery

power:

A single lithium polymer cell provides nominally 3.7v. The HP-49g+ runs off 3 AAA batteries, which provide nominally 4.5V (3x 1.5V alkalines) or 3.6V (3x 1.2V NI-MH/CD). Since people have had luck using NI-MH batteries long term, and the low battery warning doesn't come on until about 3.3V (can someone verify this?) It seems a single cell battery will be suitable.

Some people have done measurements of the current draw for various tasks. The maximum draw seems to be around 100mA, so if you want to be able to run for 10 hours at maximum draw, you need at least 1000mAh battery.

charging:

One of the more difficult aspects of using lithium ion or ploymer batteries is that they require a slightly more complicated charger (compared to trickle charging a ni-cd, or ni-mh). While there are several chargers to choose from, the MAX1555 from Maxim Semiconductor fit the bill perfectly.

Pros:

• Small package
• Designed to charge from a USB port (with the proper 100ma current limiter)
• Designed to charge single cell batteries (3.7V)
• no supporting components needed (like caps or resistors, which would have been annoying)
• Manages it's own temperature

Con(s):

• Small package: the SOT-23 surface mount package is rather difficult to solder, and you'll need to connect your wires to something. Fortunately, there are adapters which at least help you connect the wires, though you'll still have to solder the charger to the adapter.
  

ordering:

I bought everything that I needed for this project from a little company called Spark Fun Electronics, as they had everything I needed for good prices.

The MAX1555 can be had directly from Maxim, but other suppliers should have it.

The lithium battery can also be had from almost anywhere.

As for other stuff, I already had some wire laying around, and soldering supplies. Since I wanted to keep the battery compartment for AAAs, I also bought a switch, a couple small caps , and the adapter for the MAX1555 (to make soldering connections easier).

procedure:

First, let me make it clear that I know what the best documentation is made while actually doing the proecedure, as opposed to after. But, I was too excited, so you'll have to go by my pictures from after the fact. This isn't a rigiorus procedure, as it's pretty obvious what needs to get connected to what, and you can figure out where and how. So, here are pictures of what I ended up doing for various steps.

Here is my HP-49g+ calculator. to open it, I cut an old credit card in half, so I had a decent piece of plastic that had a relatively sharp cut corner. I pried this between the black bottom cover, and the gold top cover. Pressing hard, the two pieces separated, and I was able to work my plastic credit card tool around the whole case and separate the two halves.

This is the inside of the modified calculator, but the inside of your stock calculator should look similar (wires and stuff) At least on mine, the speakers (the gold disk in the lower left) didn't have a long enough wire to stay attached to the back case (in the lower right of the picture) so I had to pry it out. When I put it back together, I stick it back in place with electrical tape.

Now is a good time to cut a hole for the switch, glue it into place and wire it up with the positive wires from your Lithium Polymer batter and the existing wire from the alkalines on either side, and the wire for the positive power input for on the circuit board in the middle

Here you can see where the ground and positive USB charging wires for MAX1555 go on the mini-usb port. As far as I know these wires are unused on the 45g+, but they can be used to power the calculator in the 50g. Since the USB spec says that 100mA are available without asking for more, and the charger is designed to use all of this, you're on your own as far as USB specs go if you use a 50g.

I mounted the MAX1555 on a small board (mentioned above) and here I have the wires connected. (see the documentation for the MAX1555 to see what wires go where)

I wrapped the little board with the MAX1555 with electrical tape and taped it into an unused space inside the calculator. There are better ways, but this works.

The new lithium polymer battery tucked away below the meal shield.

I'm not sure if it's needed or not, but since the alkalines had a capacitor in parallel, I put two small capacitors in parallel with the new battery. Anyway, it doesn't hurt anything. (I tied together the negative terminals on the batteries and the calculator, so these caps really are in parallel with the new battery.

Finished product:

Toss the battery cover back on, hit "on" and off you go. I guess you could charge the battery too. There is an application other there somewhere that lets you know your battery voltage, so you'll be able to see when it's done charging.