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Share-based Payments - Share-based Compensation Expense Recognized (Details) - USD ($)
$ in Millions
12 Months Ended
Aug. 31, 2025
Aug. 31, 2024
Aug. 31, 2023
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based payment expense $ 45.1 $ 46.6 $ 42.0
Stock Incentive Plan      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based payment expense 45.1 46.6 42.0
Restricted stock awards and units | Stock Incentive Plan      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based payment expense 24.0 23.9 19.6
Performance stock units | Stock Incentive Plan      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based payment expense 18.9 18.6 15.2
Stock options | Stock Incentive Plan      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based payment expense 0.7 2.6 5.7
Director stock units | Stock Incentive Plan      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based payment expense $ 1.5 $ 1.5 $ 1.5