In principle there's often no reason why a library shouldn't work with normal Java code, but since the BETA libraries are instantiated with a reference to a PApplet object you still need to have the Processing libraries:

Code:

public BoringLibrary(PApplet parent) {
    this.parent = parent;
    ...
} 

If the library doesn't actually use the PApplet object, you could pass it a null reference and use it as normal. I doubt you'll have much luck though.

You could try writing the person who wrote Maxlink and see if he is willing to give you the code. Ideally, library writers should release their source code under GPL so that it would be possible to recycle code for use outside of Processing as well.

Reinventing the wheel is the most tedious part of computational work. Being able to see the code also helps understanding the inner workings of the library, particularly for coders who are developing their work in Eclipse or other straight Java IDEs. My work certainly got easier when the Processing source became openly available.

But a single call to PApplet.println(), PApplet.random() or any other convenience method will necessitate an actual PApplet instance. With Maxlink I would guess that it doesn't need an actual canvas, in which case one could instantiate a dummy PApplet to act as a host to the library, even if it never gets displayed.

You will need to put it in your classpath, depending on your tool there are several ways of doing this. You also need to give your application access to the processing.core libraries so it can find PApplet etc.

Read REAS' post on integrating Eclipse with the Processing JARs for some good leads.

Good luck!