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Income Taxes (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
May 31, 2025
May 31, 2024
May 31, 2025
May 31, 2024
Aug. 31, 2024
Income Tax Disclosure [Abstract]          
(Benefit) provision for income taxes 23.60% 23.20% 5.90% 23.10%  
Decrease in effective tax rate     17.20%    
Expiration of statute of limitations, release of uncertain tax position     $ 11.9    
Income taxes receivable $ 4.5   $ 4.5   $ 0.5