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Positive direction for Reaction Forces is up, for Reaction Moments is by clockwise. beam@orlovsoft.com (for new scheme).
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Reactions:

R_{A} = \frac{1}{2} \frac{F b (2 b^{2} + 3 a^{2} + 6 a b)}{b^{3} + 3 b^{2} a + 3 a^{2} b + a^{3}}

R_{B} = \frac{1}{2} \frac{(2 a + 3 b) a^{2} F}{b^{3} + 3 b^{2} a + 3 a^{2} b + a^{3}}

M_{A} = - \frac{1}{2} \frac{(a + 2 b) b a F}{a^{2} + 2 a b + b^{2}}

Shearing Forces:

Q_{1} = \frac{1}{2} \frac{F b (2 b^{2} + 3 a^{2} + 6 a b)}{b^{3} + 3 b^{2} a + 3 a^{2} b + a^{3}}

Q_{2} = - \frac{1}{2} \frac{(2 a + 3 b) a^{2} F}{b^{3} + 3 b^{2} a + 3 a^{2} b + a^{3}}

Bending Moments:

M_{1} = - \frac{1}{2} \frac{(a^{3} - 3 a^{2} z + 3 a^{2} b - 6 a z b + 2 b^{2} a - 2 z b^{2}) b F}{(a^{2} + 2 a b + b^{2}) (a + b)}

M_{2} = \frac{1}{2} \frac{(2 a + 3 b) a^{2} F (- z + b)}{b^{3} + 3 b^{2} a + 3 a^{2} b + a^{3}}

Bending Angles:

ϕ_{1} = - \frac{1}{4} \frac{(2 a^{3} - 3 a^{2} z + 6 a^{2} b - 6 a z b + 4 b^{2} a - 2 z b^{2}) F b z}{J_{x} E (b^{3} + 3 b^{2} a + 3 a^{2} b + a^{3})}

ϕ_{2} = \frac{1}{4} \frac{a^{2} F (- 2 z^{2} a - 3 z^{2} b + 4 a z b + 6 z b^{2} - 2 b^{3} + a^{2} b)}{J_{x} E (b^{3} + 3 b^{2} a + 3 a^{2} b + a^{3})}

Deflections:

w_{1} = - \frac{1}{12} \frac{(3 a^{3} - 3 a^{2} z + 9 a^{2} b - 6 a z b + 6 b^{2} a - 2 z b^{2}) F b z^{2}}{J_{x} E (b^{3} + 3 b^{2} a + 3 a^{2} b + a^{3})}

w_{2} = - \frac{1}{12} \frac{a^{2} F (2 z^{3} a + 3 z^{3} b - 6 z^{2} b a - 9 z^{2} b^{2} + 6 z b^{3} - 3 z b a^{2} + 3 a^{2} b^{2} + 4 b^{3} a)}{J_{x} E (b^{3} + 3 b^{2} a + 3 a^{2} b + a^{3})}

Numeric Sample (Maple input data): a:=2: b:=1: F:=3000: E:=2*10^11: J[x]:=200*10^(-8): q:=1000:
Structural analysis software sample 4

Reactions:

R_{A} = \frac{1}{8} \frac{q a (8 b^{3} + 24 a b^{2} + 20 a^{2} b + 5 a^{3})}{b^{3} + 3 a b^{2} + 3 a^{2} b + a^{3}}

R_{B} = \frac{1}{8} \frac{q a^{3} (4 b + 3 a)}{b^{3} + 3 a b^{2} + 3 a^{2} b + a^{3}}

M_{A} = - \frac{1}{8} \frac{(a^{2} + 4 a b + 4 b^{2}) q a^{2}}{a^{2} + 2 a b + b^{2}}

Numeric Sample (Maple input data): a:=2: b:=1: F:=1000: E:=2*10^11: J[x]:=200*10^(-8): q:=1000:
Structural analysis software sample 5

Reactions:

R_{A} = - \frac{1}{8} \frac{- 8 b^{3} q a - 20 b a^{3} q - 24 b^{2} q a^{2} - 5 q a^{4} + 12 b a^{2} F + 8 b^{3} F + 24 a b^{2} F}{b^{3} + 3 a^{2} b + 3 b^{2} a + a^{3}}

R_{B} = - \frac{1}{8} \frac{a^{2} (- 4 b q a + 12 b F - 3 q a^{2} + 8 a F)}{b^{3} + 3 a^{2} b + 3 b^{2} a + a^{3}}

M_{A} = \frac{1}{8} \frac{(- q a^{3} - 4 b q a^{2} - 4 b^{2} q a + 4 a b F + 8 b^{2} F) a}{a^{2} + 2 a b + b^{2}}

Numeric Sample (Maple input data): a:=2: b:=1: F:=3000: E:=2*10^11: J[x]:=200*10^(-8): q:=1000:
Structural analysis software sample 6