I didn't find any site that translates these verbs in the mathematical sense. What are the Latin translations of these terms, and are there any sites that offer Latin translations of modern mathematical terminology?
It helps that differential calculus was invented at a time when mathematical works were still regularly published in Latin. From Leonhard Euler's Institutiones Calculi Differentialis (1755), caput IV, p. 115 (PDF):
Ex voce autem differentialis, qua differentia infinite parua denotatur, alia nomina deriuantur, quae vsu sunt recepta. Sic verbum habetur differentiare, quod significat differentiale inuenire, quantitasque differentiari dicitur, quando eius differentiale elicitur. Differentiatio autem denotat operationem, qua differentialia inueniuntur. Hinc calculus differentialis quoque vocatur methodus differentiandi, cum modum differentialia inueniendi contineat.
From the expression differentialis, which is what we call infinitely small differences, derive several other words that have come into use. Thus we have the verb differentiare, which means to find the differential, and one says quantities are being differentiated [Euler simply explains the passive form here] when their differential is determined. Differentiatio then denotes the operation by which differentials are found. Thus the differential calculus is also called the method of differentiating [Euler explaining the gerund], since it contains a way to find differentials.
In the same way as the differential function is called differentiale, the integral is called integrale and the process of finding it integratio, which is clear from many examples in the text, although I found no similarly nice paragraph explicating these terms. It stands to reason that the associated verb would be integrare, which is also a classically attested verb without a specifically mathematical meaning, but that should be no hindrance.
I found no word for “parameterizing” (and don't really know where to look for it either). Parameterizatio seems obvious, but does not seem to exist.