Please capitalize where necessary: even after the purchase of your machine, it is still our goal to ensure that it operates perfectly.
A: Even after the purchase of your machine, it is still our goal to ensure that it operates perfectly.

Please capitalize where necessary: where s is the distance between point z and point ζ.
A: where s is the distance between point Z and point ζ.

Please capitalize where necessary: the boat paints are just as usable as water under water.
A: The boat paints are just as usable as water under water.

Please capitalize where necessary: it was so, that, when those who bore the ark of yahweh had gone six paces, he sacrificed an ox and a fattened calf.
A:
It was so, that, when those who bore the ark of Yahweh had gone six paces, he sacrificed an ox and a fattened calf.