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Income Taxes - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
Income Taxes - Narrative (Details) - USD ($) $ in Millions	Aug. 31, 2026	Aug. 31, 2025	Aug. 31, 2024	Aug. 31, 2023
Income Tax Contingency [Line Items]
Income tax paid, after refund received	$ 107.6	$ 151.8	$ 155.7
Deferred income tax liability for certain foreign withholding taxes and U.S. state taxes	0.4
Unrecognized tax benefits	18.7	18.5	21.1	$ 20.1
Unrecognized tax benefits that if recognized would affect annual effective tax rate	18.7	18.5
Total accrued interest	2.3	$ 2.4	$ 4.6
Accruals related to income tax penalties	0.7
Internal Revenue Service (IRS)
Income Tax Contingency [Line Items]
Federal tax credit carryforwards, subject to expiration	14.7
Tax credit carryforward subject to a full valuation allowance	7.7
Income Tax Jurisdiction, Domestic State and Local
Income Tax Contingency [Line Items]
Federal tax credit carryforwards, subject to expiration	0.3
Operating loss carryforwards	27.9
Non-US:
Income Tax Contingency [Line Items]
Operating loss carryforwards	$ 18.6