Try something like this:

from mpmath import *
mp.dps = 30; mp.pretty = True

f=[lambda s00, s01, s10, s11, k, p:0.55*k*s00 + 0.6*k*s01 + 0.6*k*s10
+ 0.6*p*s01 + 0.6*p*s10 +0.55*p*s11 + 33*s00 + 33*s01 + 33*s10 +
33*s11 - 33.0,
lambda s00, s01, s10, s11, k, p:0.55*k*s00 + 0.6*k*s01 + 0.6*k*s10 +
33*k - 0.33,
lambda s00, s01, s10, s11, k, p:0.6*p*s01 + 0.6*p*s10 + 0.55*p*s11 +
33*p - 0.33,
lambda s00, s01, s10, s11, k, p:0.11*k*s00 - 0.06*p*s01 - 0.06*p*s10,
lambda s00, s01, s10, s11, k, p:(0.06*k + 0.06*p)*s01 - 0.055*k*s00 -
0.055*p*s11,
lambda s00, s01, s10, s11, k, p:(0.06*k + 0.06*p)*s10 - 0.055*k*s00 -
0.055*p*s11]


s= findroot(f,(0.1,0.1,0.1,0.1,0.1,0.1))
print [round(s[k,0],10) for k in range(6)]

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