Organopolysiloxane, powder treatment agent, and treated powder and cosmetic treated with powder treatment agent

An organopolysiloxane represented by the following average structural formula (1):

• wherein, in the formula (1), each R independently represents a group selected from a hydrogen atom, a hydroxy group, an alkyl group having 1 to 30 carbon atoms, a fluoroalkyl group having 1 to 12 carbon atoms, an aryl group having 6 to 12 carbon atoms, and an aralkyl group having 7 to 12 carbon atoms, and each R10 independently represents a group defined by the following average structural formula (2):
• wherein, in the formula (2), X is a divalent hydrocarbon group having 1 to 10 carbon atoms, s is a number of 1 to 100, t is a number of 0 to 50, the bonding arrangement of oxyalkylene units each identified by s and t in brackets may be blocked or random, v is a number of 1 to 10, each R12 independently represents a group selected from an alkyl group having 1 to 6 carbon atoms and an aryl group having 6 to 12 carbon atoms, each R13 independently represents a hydrogen atom or a monovalent hydrocarbon group having 1 to 6 carbon atoms, and w is a number of 0 to 2;
• wherein R11 is a group selected from R10 or R, and each A independently represents an organopolysiloxane segment defined by the following average structural formula (3) or (4):
• wherein, in the formula (3), R and R10 are as defined above, c is a number of 0 to 3, i is a number of 0 to 10, j is a number of 0 to 100, and Q is an oxygen atom or a divalent hydrocarbon group having 1 to 3 carbon atoms, and in the formula (4), X is as defined above, and the bonding arrangement of siloxane units each identified by i and j in brackets may be blocked or random, and
• wherein, in the formula (1), each of a and b independently represents a number of 0 to 3, e is a number of 0 to 50, f is a number of 0 to 2,000, g is a number of 0 to 10, h is 0 or 1, the bonding arrangement of siloxane units each identified by e, f, g and h in brackets may be blocked or random, and one or more R10s are present in the formula (1).