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.