I use PlastStrut brand of styrene cement. They make a couple of kinds.  The one with the orange label works on more kinds of plastic than the white label so I use the orange label.  The cement works by
dissolving a thin layer of the styrene on each part. The the soft plastics "mix" and the parts are bonded when the cement evaporates. This cement is thin and evaporates quickly so you will need to be generous in application. Although I'm working on the cutting mat, be warned that this cement will soften the cutting mat surface so be careful or work on a different surface.