I would like recommendations for a good calculus book that isn't as math centered as Spivak, nor as dumb as Stweart, that has decent theory and challenging PRACTICAL problems (less "Prove that...").
Edit: I don't want something with too much focus on axiomatic treating and theorem proving. I'm looking for a less mathematical book, focused on applying techiniques to solve uncommon limits, derivatives and integrals, as well as applications to science and engineering.
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You might look at Adam's Calculus. I didn't think it was the best book for the class I was teaching, but I considered it harder than Stewart or Anton. There are more-than-average number of applications. It's a Canadian text, so you have to put up with bizarre spellings of words like "center" and "liter". And all word problems are in a a deviate measuring system called "metric". Otherwise, it might be what you're looking for.
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If you think Steward's Calculus is dumb, you might be interested in Multivariable Mathematics by Ted Shifrin. It is not introductory but contains a lot of examples.
I recommend Zorich's mathematical analysis. It is clear and contains lots of examples.