This is the 2008th most frequent Russian word.
установленных
"Established" or "set."
The word 'установленных' in this sentence functions as an adjective in the genitive plural form, used to describe the noun 'правил' (rules), indicating that the rules are those that have been established.
Соблюдение установленных правил обязательно.
Compliance with established rules is mandatory.
Here, 'установлены' is used as a past passive participle in plural form derived from the verb 'установить', meaning 'installed'.
Камеры были установлены на всех углах здания.
Cameras were installed on all corners of the building.
In this context, 'установленных' again functions as an adjective in the genitive plural form, modifying the noun 'задач' (tasks) to indicate that the tasks are those defined or established previously.