I perform magic on a somewhat regular basis. I assume that it has the power to actually affect change in the world or I wouldn't bother. So assuming it works (at least some of the time) I have a couple of questions:
Do you feel magic is more effective when coupled with religion, or separated from it? Do you pray (to anyone/thing) for favors or success? Do you ask that other entities carry out action on your behalf? Is this really magic, or is it worship? If you practice non-religious magic do you believe that the energy comes from within you or without you?
I think that different types of magic need different approaches. For me long term magic for personal or community/environmental/human change benefits greatly from the involvement of "higher order" entities of various types. "Low magic", which tends to be practical and non-religious, suits itself to everyday living, especially to improving material circumstances.
I do sometimes pray for protection or strength, sometimes for myself, generally for others. I do not consider this to be either religion or magic, perhaps "prayer" is independent of these things. The only action I tend to ask for is a guiding hand.
When I perform magic without prayer I tend to draw energy from the objects I use, the elements, the earth, the universe. Rarely do I use personal energy for this type of thing, as I find it draining.