Business Segments (Schedule of Revenue by Geographical Areas) (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2025	Aug. 31, 2024	Aug. 31, 2023
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenues	$ 676,368	$ 607,074	$ 674,084
Geographic Concentration [Member] | Revenues [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenues	$ 676,368	$ 607,074	$ 674,084
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	$ 142,307	$ 112,815	$ 99,681
Geographic Concentration [Member] | United States [Member] | Revenues [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenues	$ 350,229	$ 338,429	$ 347,238
Percentage	52.00%	56.00%	52.00%
Geographic Concentration [Member] | United States [Member] | Long-Lived Tangible Assets [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Percentage	82.00%	79.00%	77.00%
Long-lived tangible assets	$ 116,771	$ 89,175	$ 76,428
Geographic Concentration [Member] | International [Member] | Revenues [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenues	$ 326,139	$ 268,645	$ 326,846
Percentage	48.00%	44.00%	48.00%
Geographic Concentration [Member] | International [Member] | Long-Lived Tangible Assets [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Percentage	18.00%	21.00%	23.00%
Long-lived tangible assets	$ 25,536	$ 23,640	$ 23,253