Please capitalize where necessary: the other firm firm might manufacture all of the components for its calculators.
A: The other firm firm might manufacture all of the components for its calculators.

Please capitalize where necessary: more troubling is the upcoming book by ben mezrich (the ben mezrich who lionized the mit blackjack card-counting team and facebook founders) straight flush.
A: More troubling is the upcoming book by Ben Mezrich (the Ben Mezrich who lionized the MIT Blackjack Card-Counting Team and Facebook founders) Straight Flush.

Please capitalize where necessary: list of all star players on the team is found at "players", "stars".
A: List of all star players on the team is found at "Players", "Stars".

Please capitalize where necessary: he was introduced to modern analysis by young and after this he began to make a real contribution to research.
A:
He was introduced to modern analysis by Young and after this he began to make a real contribution to research.