I'm sure we all know about the metamagic feat Maximize Spell, which allows you to cast a spell in a slot 3 levels higher in order to "maximize all variable numeric values" like damage, number of targets, etc, but what effect does that have on spells like Prismatic Spray, whose "variable numeric values" change its effects entirely? Would the color roll default to 8, then from there to 7 and 6, or would Maximize simply not have any effect on these spells?
You're not correctly quoting the feat. It reads as follows:
The key word to adjudicate this is effects. The die roll is not an effect, it's something the player does when they cast the spell. And which particular ray is chosen is not numeric -- it's a qualitative, not quantitative, effect.
20d6 + 20 damage, 1d3 summoned creatures, or a duration of 1d6 rounds would all be things that might be maximized. They're variable, numeric effects of the spell.
(And to be more accurate, I might describe it as 40-140 damage, 1–3 creatures, or 1–6 rounds; again, the die rolls are only how you determine the number.)
I’d argue (though I have seen it argued oppositely) that the Maximize Spell does not maximize all rolls, just rolls used to set numerical values. The roll in a prismatic spell doesn’t set a numerical value, it picks an effect, and therefore is not affected.
Considering that you would otherwise get an infinite loop as all rolls are maximized and demand you to continue rolling twice and keeping both (and both are maximized), that’s probably for the best.