trotz starken Regens, wegen hoher Preise — the Genitiv with no article.
Every line is Genitiv — after trotz, wegen, während, aufgrund, statt, innerhalb. Type the missing endings; the noun's gender is shown.
trotz guten Essens, wegen starken Regens. The one place the adjective doesn't copy der/das: the noun already ends in -s or -es, so the adjective takes -en.
trotz großer Hitze. Like der in 'der Hitze' — and the noun doesn't change.
wegen hoher Kosten. Like der in 'der Kosten'.
With an article in front, the article shows the Genitiv (des, der, eines, einer, meiner …) and the adjective just takes -en.
All Genitiv, all mixed: with or without an article, any gender.