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Industry Segment Information (Schedule of Revenue by Geographical Areas) (Details) - USD ($)
$ in Thousands
12 Months Ended
Aug. 31, 2024
Aug. 31, 2023
Aug. 31, 2022
Revenues from External Customers and Long-Lived Assets [Line Items]      
Revenues $ 607,074 $ 674,084 $ 770,743
Geographic Concentration [Member] | Revenues [Member]      
Revenues from External Customers and Long-Lived Assets [Line Items]      
Revenues $ 607,074 $ 674,084 $ 770,743
Percentage 100.00% 100.00% 100.00%
Geographic Concentration [Member] | Long-Lived Tangible Assets [Member]      
Revenues from External Customers and Long-Lived Assets [Line Items]      
Percentage 100.00% 100.00% 100.00%
Long-lived tangible assets $ 112,815 $ 99,681 $ 94,472
Geographic Concentration [Member] | United States [Member] | Revenues [Member]      
Revenues from External Customers and Long-Lived Assets [Line Items]      
Revenues $ 338,429 $ 347,238 $ 394,080
Percentage 56.00% 52.00% 51.00%
Geographic Concentration [Member] | United States [Member] | Long-Lived Tangible Assets [Member]      
Revenues from External Customers and Long-Lived Assets [Line Items]      
Percentage 79.00% 77.00% 75.00%
Long-lived tangible assets $ 89,175 $ 76,428 $ 70,643
Geographic Concentration [Member] | International [Member] | Revenues [Member]      
Revenues from External Customers and Long-Lived Assets [Line Items]      
Revenues $ 268,645 $ 326,846 $ 376,663
Percentage 44.00% 48.00% 49.00%
Geographic Concentration [Member] | International [Member] | Long-Lived Tangible Assets [Member]      
Revenues from External Customers and Long-Lived Assets [Line Items]      
Percentage 21.00% 23.00% 25.00%
Long-lived tangible assets $ 23,640 $ 23,253 $ 23,829