Goodwill and Intangible Assets - Narrative (Details) - USD ($) $ in Millions	3 Months Ended	9 Months Ended
May 31, 2026	May 31, 2025	May 31, 2026	May 31, 2025
Intangible Asset, Goodwill and Other [Abstract]
Amortization of intangible assets	$ 23.0	$ 20.0	$ 70.4	$ 45.5

Amount of amortization expense for finite-lived intangible asset. Excludes goodwill and capitalized cost for software to be sold, leased, or marketed.

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