Questions about how Mathematica evaluates expressions, tracing evaluation (Trace*), handling expressions in unevaluated form (Hold*, Unevaluated), nonstandard evaluation, etc.

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Define a Plot3D function with custom options [duplicate]

I am trying to define a Plot3D function with custom options, following (this previous SE question), but I'm running into a brick wall. I've narrowed the problem to the following 'toy' code: ...
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How to ContourPlot a Table? [duplicate]

Possible Duplicate: Why is ContourPlot not displaying this curve? Why do I have to put Evaluate[] here I'm trying to plot certain contours of a function $f:\mathbb R^2\to\mathbb R$. What I ...
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Why doesn't Mathematica evaluate this limit?

I am trying to evaluate a few limits in Mathematica, and I can only get it to evaluate them in certain cases. I don't fully understand the evaluation order and when it substitutes numerical values in ...
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Find the value by using FindRoot command [closed]

The equation x^4-3 x^3 = cos(3x)+3 has two real solutions on the interval from -10 to 10. Lets call these two solutions r and s. Use Mathematica's FindRoot command to find r and s. Now let M equal the ...