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Stock-Based Compensation Expense and Shareholders' Equity (Details Textual) - USD ($)
 1 Months Ended 3 Months Ended 12 Months Ended
Dec. 19, 2023
Dec. 20, 2022
Dec. 31, 2024
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
Apr. 30, 2023
Jul. 31, 2025
Jul. 31, 2024
Jul. 31, 2023
Dec. 15, 2020
Class of Stock [Line Items]                      
Total stock-based compensation expense               $ 161,556,000 $ 146,460,000 $ 142,842,000  
Granted (in USD per share)               $ 63.29      
Common stock, shares authorized (in shares)               500,000,000 500,000,000    
Common stock, par value (in dollars per share)               $ 0.0001 $ 0.0001    
Common stock, shares, issued (in shares)               84,530,418 83,025,637    
Common stock, shares outstanding (in shares)               84,530,418 83,025,637    
Payments for repurchase of common stock               $ 0 $ 0 $ 261,807,000  
Treasury Stock, Shares, Acquired                   4,041,284  
Treasury Stock Acquired, Average Cost Per Share                   $ 64.78  
Accelerated Share Repurchase Agreement                      
Class of Stock [Line Items]                      
Authorized amount           $ 400,000,000          
Remaining authorized amount               138,200,000      
Payments for repurchase of common stock           $ 200,000,000          
Treasury Stock, Shares, Acquired           2,581,478 648,001     3,229,479  
Treasury Stock Acquired, Average Cost Per Share                   $ 61.93  
Stock awards                      
Class of Stock [Line Items]                      
Period of time based vesting       3 years 3 years            
Award performance period       3 years 3 years            
Performance Shares                      
Class of Stock [Line Items]                      
Period of time based vesting                 3 years    
Total stock-based compensation expense               $ 26,200,000 $ 16,200,000 $ 15,000,000  
Performance Shares | Tranche One                      
Class of Stock [Line Items]                      
Vesting percentage                 50.00%    
Performance Shares | Tranche Two                      
Class of Stock [Line Items]                      
Vesting percentage                 50.00%    
ESPP                      
Class of Stock [Line Items]                      
Number of shares authorized (in shares)     3,000,000                
Share-Based Compensation Arrangement by Share-Based Payment Award, Purchase Price of Common Stock, Percent     85.00%                
ESPP | Minimum                      
Class of Stock [Line Items]                      
Share-Based Compensation Arrangement by Share-Based Payment Award, Maximum Employee Subscription Rate     1.00%                
ESPP | Maximum                      
Class of Stock [Line Items]                      
Share-Based Compensation Arrangement by Share-Based Payment Award, Maximum Employee Subscription Rate     15.00%                
Stock Plan 2020                      
Class of Stock [Line Items]                      
Number of shares authorized (in shares)                     5,000,000
Number of additional shares authorized (in shares) 3,800,000 1,780,000