你只把case这个词放在case表达式的开头。只需删除第二份和随后的副本。所以你的第一个触发点是：

BEGIN
    UPDATE `incent` a INNER JOIN `inc_prog` b  
    SET a.`earned` =
        CASE WHEN a.incactualn < b.n1 THEN 0 
             WHEN a.incactualn  BETWEEN b.n1 AND b.m1 THEN b.arp1
             WHEN a.incactualn  BETWEEN b.n2 AND b.m2 THEN b.arp1+b.arp2
             WHEN a.incactualn  BETWEEN b.n3 AND b.m3 THEN b.arp1+b.arp2+b.arp3
             WHEN a.incactualn  BETWEEN b.n4 AND b.m4 THEN b.arp1+b.arp2+b.arp3+b.arp4
             WHEN a.incactualn  BETWEEN b.n5 AND b.m5 THEN b.arp1+b.arp2+b.arp3+b.arp4+b.arp5
        END;
END

在第二次尝试中，缺少case表达式结尾处的结尾，以及子查询周围的（select and）：

BEGIN
    UPDATE a    
    SET a.earned = (SELECT
        CASE WHEN a.incactualn < b.n1 THEN '0' 
             WHEN a.incactualn  BETWEEN b.n1 AND b.m1 THEN b.arp1
             WHEN a.incactualn  BETWEEN b.n2 AND b.m2 THEN b.arp1+b.arp2
             WHEN a.incactualn  BETWEEN b.n3 AND b.m3 THEN b.arp1+b.arp2+b.arp3
             WHEN a.incactualn  BETWEEN b.n4 AND b.m4 THEN b.arp1+b.arp2+b.arp3+b.arp4
             WHEN a.incactualn  BETWEEN b.n5 AND b.m5 THEN b.arp1+b.arp2+b.arp3+b.arp4+b.arp5
        END
    FROM incent a
    INNER JOIN inc_prog b ON a.Incent_name = b.incname && a.period = b.finyear);
END