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Michael E2
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I am having a same problem on Linux, Mathematica 10.0.01. My "solution" (if you are looking for it?) for dashing of the frame was to specify each frame part individually:

b = Plot[{x, x^2}, {x, 0, 10}, Frame -> True,
   FrameStyle -> {{Dashing[1], Dashing[1]}, {Dashing[1], Dashing[1]}}, PlotTheme -> "Monochrome""Monochrome"]

enter image description here

Very annoyingly, if I try to do the same trick to fill plot lines, one of them gets "cut"

b = Plot[{x, x^2}, {x, 0, 10}, Frame -> True,
   FrameStyle -> {{Dashing[1], Dashing[1]}, {Dashing[1], Dashing[1]}},
   PlotStyle -> {Dashing[1], Dashing[1]}, PlotTheme -> "Monochrome"]

enter image description here

I am having a same problem on Linux, Mathematica 10.0.01. My "solution" (if you are looking for it?) for dashing of the frame was to specify each frame part individually:

b = Plot[{x, x^2}, {x, 0, 10}, Frame -> True,  FrameStyle -> {{Dashing[1], Dashing[1]}, {Dashing[1], Dashing[1]}}, PlotTheme -> "Monochrome"

enter image description here

Very annoyingly, if I try to do the same trick to fill plot lines, one of them gets "cut"

b = Plot[{x, x^2}, {x, 0, 10}, Frame -> True, FrameStyle -> {{Dashing[1], Dashing[1]}, {Dashing[1], Dashing[1]}}, PlotStyle -> {Dashing[1], Dashing[1]}, PlotTheme -> "Monochrome"]

enter image description here

I am having a same problem on Linux, Mathematica 10.0.01. My "solution" (if you are looking for it?) for dashing of the frame was to specify each frame part individually:

b = Plot[{x, x^2}, {x, 0, 10}, Frame -> True,
   FrameStyle -> {{Dashing[1], Dashing[1]}, {Dashing[1], Dashing[1]}}, PlotTheme -> "Monochrome"]

enter image description here

Very annoyingly, if I try to do the same trick to fill plot lines, one of them gets "cut"

b = Plot[{x, x^2}, {x, 0, 10}, Frame -> True,
   FrameStyle -> {{Dashing[1], Dashing[1]}, {Dashing[1], Dashing[1]}},
   PlotStyle -> {Dashing[1], Dashing[1]}, PlotTheme -> "Monochrome"]

enter image description here

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I am having a same problem on Linux, Mathematica 10.0.01. My "solution" (if you are looking for it?) for dashing of the frame was to specify each frame part individually:

b = Plot[{x, x^2}, {x, 0, 10}, Frame -> True,  FrameStyle -> {{Dashing[1], Dashing[1]}, {Dashing[1], Dashing[1]}}, PlotTheme -> "Monochrome"

enter image description here

Very annoyingly, if I try to do the same trick to fill plot lines, one of them gets "cut"

b = Plot[{x, x^2}, {x, 0, 10}, Frame -> True, FrameStyle -> {{Dashing[1], Dashing[1]}, {Dashing[1], Dashing[1]}}, PlotStyle -> {Dashing[1], Dashing[1]}, PlotTheme -> "Monochrome"]

enter image description here