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Income Taxes - Schedule of Reconciliation of Federal Statutory Rate to Total Provision for Income Taxes (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 31, 2024	Aug. 31, 2023	Aug. 31, 2022
Income Tax Disclosure [Abstract]
Federal income tax computed at statutory rate	$ 115.2	$ 93.8	$ 103.7
State income tax, net of federal income tax benefit	19.7	11.4	13.5
Federal permanent differences	2.1	2.2	(4.3)
Foreign permanent differences and rate differential	2.3	4.4	4.3
Research and development tax credits	(10.1)	(8.3)	(7.6)
Unrecognized tax benefits	2.0	1.9	2.1
Other, net	(5.2)	(4.7)	(1.8)
Total provision for income taxes	$ 126.0	$ 100.7	$ 109.9

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