Please capitalize where necessary: system formulated in two variants: strong regular and, depending on the type of hair two different choices for a more or less intensive treatment.
A: System formulated in two variants: STRONG REGULAR and, depending on the type of hair two different choices for a more or less intensive treatment.
Q: while there is a decline in the arctic ice there is an increase in the antarctic ice.

A: While there is a decline in the Arctic ice there is an increase in the Antarctic ice.
Q: he thought it valid only to the extent to which ideas were actually in conformity with things.
A: He thought it valid only to the extent to which ideas were actually in conformity with things.
Problem: another idea for more energy involves installing a water turbine on the pipe that leads the water to the cabins from a lake situated high up.
Can you repeat this sentence, but capitalize it?
Answer: Another idea for more energy involves installing a water turbine on the pipe that leads the water to the cabins from a lake situated high up.
Text: so far the insight has never let him down and rigorous proofs, of the standard we mathematicians rightly expect, have always been forthcoming.

Correct capitalization: So far the insight has never let him down and rigorous proofs, of the standard we mathematicians rightly expect, have always been forthcoming.
Q: fashion style multi color crystal and black velvet ribbon woven bold bracelet with extendable chain

A:
Fashion Style Multi Color Crystal and Black Velvet Ribbon Woven Bold Bracelet with Extendable Chain