The board of regents of said University of Washington are authorized, upon the filing of such plat with it, to agree in writing with any such railroad company or streetcar company, upon the boundaries and the extent of such right-of-way, the manner in which the same shall be maintained and fenced and occupied, and prescribe the number, character, and maintenance of crossings, cross-overs, and subways, and as to what sum said railroad company or streetcar company shall pay for the right-of-way granted.