Adjustable LiPo battery charging circuit

So I found myself having a lot of small 1 cell lipo batteries from various devices and gadgets I took apart (broken before or after I disassembled them) and no way to charge them. Recently I found a small boost converter to power small 5V devices. It has a USB female jack on one end and 2 solder pads on the other. It uses anything from 1.5 to 4.5V to output the needed 5V at a maximum of 450mA. The batteries I have would be great but I have no way to use them multiple times. This is the result:

DIY lipo charger

It looks ugly but it does the job great.

Using LM317T to simulate LIPO battery

I have a few battery operated devices (rechargeable) that I wouldn't mind using only connected to a power source. So I started to find a way to replace a LIPO cell with a power supply. The first (and easiest) answer to this problem is using a LM317 as a power source.

Typical LM317T usage circuit

So I started looking around for how I might build a circuit. I found a lot of information online and started building it. Before this, I still needed to know what the needed voltage is. A standard LIPO cell is rated at 3.7V.